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Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum random matrix theory predicts the probability distributions of level curvatures to be given by the Zakrzewski-Delande expressions. Motivated by growing interest in statistics of extreme (maximal or minimal) eigenvalues of disordered systems of various nature, it is natural to ask about the associated level curvatures. We show how calculating the distribution for the curvatures of extreme eigenvalues in Gaussian unitary ensemble can be reduced to studying asymptotic behaviour of orthogonal polynomials appearing in the recent work of Nadal and Majumdar. The corresponding asymptotic analysis being yet outstanding, we instead will discuss solution of a related, but somewhat simpler problem of calculating the level curvature distribution averaged over all the levels in a spectral window close to the edge of the semicircle. The method is based on asymptotic analysis of kernels associated with Hermite polynomials and their Cauchy transforms, and is straightforwardly extendable to any rotationally-invariant ensemble of random matrices.
Transport of a Brownian particle with an oscillating radius freely diffusing in an asymmetric corrugated channel was simulated over a range of driving forces for a series of temperatures and angular frequencies of radial oscillation. It was observed that there was a strong influence of self-oscillation frequency on the average particle velocity. This effect can be used to control rectification of biologically active particles as well as for their separation according to their activity, for instance in the separation of living and dead cells.
We apply the Zipf power law to financial time series of WIG20 index daily changes (open-close values). Thanks to the mapping of time series signal into the sequence of 2k+1 'spin-like' states, where k=0, 1/2, 1, 3/2, ..., we are able to describe any time series increments, with almost arbitrary accuracy, as the one of such 'spin-like' states. This procedure leads in the simplest non-trivial case (k = 1/2) to the binary data projection. More sophisticated projections are also possible and mentioned in the article. The introduced formalism allows then to use Zipf power law to describe the intrinsic structure of time series. The fast algorithm for this implementation was constructed by us within Matlab^{TM} software. The method, called Zipf strategy, is then applied in the simplest case k = 1/2 to WIG 20 open and close daily data to make short-term predictions for forthcoming index changes. The results of forecast effectiveness are presented with respect to different time window sizes and partition divisions (word lengths in Zipf language). Finally, the various investment strategies improving return of investment (ROI) for WIG20 futures are proposed. We show that the Zipf strategy is the appropriate and very effective tool to make short-term predictions and therefore, to evaluate short-term investments on the basis of historical stock index data. Our findings support also the existence of long memory in financial data, exceeding the known in the literature 3 days span limit.
An evacuation process is simulated within the Social Force Model. Thousand pedestrians are leaving a room by one exit. We investigate the stationarity of the distribution of time lags between instants when two successive pedestrians cross the exit. The exponential tail of the distribution is shown to gradually vanish. Taking fluctuations apart, the time lags decrease in time till there are only about 50 pedestrians in the room, then they start to increase. This suggests that at the last stage the flow is laminar. In the first stage, clogging events slow the evacuation down. As they are more likely for larger crowds, the flow is not stationary. The data are investigated with detrended fluctuation analysis and return interval statistics, and no pattern transition is found between the stages of the process.
A novel sp^3-bonded nanosize domain, known as a diaphite which is an intermediate state between a graphite and a diamond, is generated by the irradiation of visible laser pulse onto a graphite crystal. The sp^3 structure is well stabilized by shear displacement between neighboring graphite layers. We theoretically study the interlayer sp^3 bond formation with frozen shear displacement in a graphite crystal, using a classical molecular dynamics and a semi-empirical Brenner potential. We show that a pulse excitation under the fluctuation of shearing motion of carbons in an initial state can generate interlayer sp^3 bonds which freeze the shear, though no frozen shear appears if there is no fluctuation initially. Moreover, we investigate a pulse excitation under the coherent shearing motion and consequently obtain that the sp^3-bonded domain with frozen shear is efficiently formed. We conclude that the initial shear is important for the photoinduced sp^3 nanosize domain formation.
Plots and quantitative measures obtained from recurrence quantification analysis - recurrence rate, determinism, entropy, and trapping time, were used for the sensitive detection of transitions from laminar (regular) to turbulent (chaotic) phases in the Lorenz model periodically modulated at the onset of chaos.
We investigate the modification of the intrinsic carrier noise spectral density induced in low-doped semiconductor materials by an external correlated noise source added to the driving high-frequency periodic electric field. A Monte Carlo approach is adopted to numerically solve the transport equation by considering all the possible scattering phenomena of the hot electrons in the medium. We show that the noise spectra are strongly affected by the intensity and the correlation time of the external random electric field. Moreover, this random field can cause a suppression of the total noise power.
The field emission current fluctuation method was applied to investigate surface self-diffusion of tungsten on the (311) and (711) regions (along the zone line (211)-(100)) of a tungsten microcrystal (in the form of the field emitter tip of radius about 300 nm) in the temperature range 500-850 K. The surface diffusion parameters were obtained from spectral analysis of the current fluctuations. The results are discussed from the aspects of the substrate structure.
The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.
Transport of Brownian particle moving along a three-dimensional throat-like channel is investigated in the presence of an external constant force. The solution of the Fick-Jacobs equation in the situation is solved, and the probability current density and particle current describing the motion of particle are obtained. It is found that entropy barrier and external force can reverse the direction of particle current. The motion of Brownian particle can be tuned by the entropy barrier and the external force.
We analytically derive superstatistics (or complex statistics) that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) exhibiting transition thresholds. We measure the interevent times between excessive losses (that is, greater than some threshold) and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates themselves and a "superscaling" configuration emerges.
We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdős-Rényi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdős-Rényi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.
We investigate the presence of multifractal residual background effect for monofractal signals which appears due to the finite length of the signals and (or) due to the constant long memory the signals reveal. This phenomenon is investigated numerically within the multifractal detrended fluctuation analysis (MF-DFA) for artificially generated time series. Next, the analytical formulas enabling to describe the multifractal content in such signals are provided. Final results are shown in the frequently used generalized Hurst exponent h(q) multifractal scenario as a function of time series length L and the autocorrelation scaling exponent value γ. The obtained results may be significant in any practical application of multifractality, including financial data analysis, because the "true" multifractal effect should be clearly separated from the so called "multifractal noise" resulting from the finite data length. Examples from finance in this context are given. The provided formulas may help to decide whether one deals with the signal of real multifractal origin or not and make further step in analysis of the so called spurious or corrupted multifractality discussed in literature.
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary mechanism responsible for the observed long-range dependence and statistical properties of high volatility return intervals. By exogenous noise we mean information flow or/and order flow fluctuations. Numerical results based on the proposed model reveal that the exogenous fluctuations have to be considered as indispensable part of comprehensive modeling of the financial markets.
We study the multifractal effects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the "true" unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A difference is stressed between "naive" observed multifractal effects calculated directly within detrended multifractal analysis as the spread Δh of the generalized Hurst exponents h(q) and the more reliable unbiased multifractality received after subtraction of residual bias effects generated by nonlinear transformations of initial data and coupled with finite size effects in time series. This property is investigated for volatile series of the real main world financial indices. A difference between multifractal properties of intraday and interday quotes is also pointed out in this context for the Warsaw Stock Exchange WIG index. Finally, based on the observed feature of real nonstationary data, a new measure of unbiased multifractality in signals is introduced. This measure comes from an analysis of the whole generalized Hurst exponent profile instead of looking just at its edge behavior h^{±} ≡ h(q→ ±∞). Such an approach seems to be particularly useful when h(q) is not a monotonic function of the moment order q. Interesting examples with extreme events from finance are presented. They convince that an analysis directed only on investigation of the edges h^{±} in multifractal spectrum may be misleading.
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