Stochastic resonance in a bias monostable system driven by a periodic rectangular signal and uncorrelated noises

The stochastic resonance in a bias monostable system driven by a periodic rectangular signal and uncorrelated noises is investigated by using the theory of signal-to-noise (SNR) in the adiabatic limit. The analytic expression of the SNR is obtained for arbitrary signal amplitude without being restricted to small amplitudes. The SNR is a nonmonotonic function of intensities of multiplicative and additive noises and the noise intensity ratio R=D/Q, so stochastic resonance exhibits in the bias monostable system. We investigate the effect of any system parameter (such as D,Q,R,r) on the SNR. It is shown that the SNR is a nonmonotonic function of the static asymmetry r, also; the SNR is decreased when |r| is increased. Moreover, the SNR is increased when the noise intensity ratio R=D/Q is increased.     

An outlier-robust kernel RLS algorithm for nonlinear system identification

In this paper, we propose multivariate multiscale permutation entropy (MMPE) and multivariate weighted multiscale permutation entropy (MWMPE) to explore the complexity of the multivariate time series over multiple different time scales. First, we apply these methods to the simulated trivariate time series which is compose of white noise and 1/f noise to test the validity of multivariate methods. The standard deviations of weighted methods are bigger because of containing more amplitude information, while the standard deviations of multivariate method are smaller than the method for single channel. Hence, it can be found that MWMPE shows a better distinguish capacity, while it is able to measure the complexity of the multichannel data accurately and reflect more information about the multivariate time series as well as holds a better robustness. Then MMPE and MWMPE methods are employed to the financial time series: closing prices and trade volume, from different area. It can be verified that the methods for multichannel data analyze the properties of multivariate time series comprehensively. The entropy values taking the weight into account for both the multichannel and single channel amplify the local fluctuation and reflect more amplitude information. The MWMPE maintain the fluctuation characteristic of SCWMPE of both price and volume. The MWMPE results of these stock markets can be divided into three groups: (1) S&P500, FTSE, and HSI, (2) KOSPI, and (3) ShangZheng. The weighted contingency also shows the difference of inhomogenity of the distributions of ordinal patterns between these groups. Thus, MWMPE method is capable of differentiating these stock markets, detecting their multiscale structure and reflects more information containing in the financial time series.     

Noise in the measurements of magnetic susceptibilities

Three methods of measuring diamagnetic susceptibilities are compared with respect to sensitivity.(1) The balance method is limited in sensitivity by thermal noise with a signal to noise ratio SNR of 3×10⁸.(2) The inductance method is limited by the Nyquist noise with an SNR of 5×10⁴.(3) The magnetometer method is very insensitive with an SNR of 40 due to Barkhausen noise.Department of Physics.Department of Electrical Engineering.     

An investigation of LDV velocity bias correction techniques for high-speed separated flows

An experimental study of the effects of velocity bias in single realization laser Doppler velocimetry measurements in a high-speed, separated flow environment is reported. The objective of the study is to determine a post-facto correction method which reduces velocity bias after individual realization data have been obtained. Data are presented for five velocity bias correction schemes: inverse velocity magnitude weighting, interarrival time weighting, sample and hold weighting, residence time weighting, and the velocity-data rate correlation method. These data were compared to a reference measurement (saturable detector sampling scheme); the results show that the interarrival time weighting method compares favorably with the reference measurement under the present conditions.     

A measure of complexity based on the order patterns

Cumulative Tsallis entropy (CE) is a recently introduced entropy metric to quantify the uncertainty of time series, and its expressions of continuous random variable and discrete random variable are consistents. So far, it has proved to have a good performance in the characteristics of time series. This paper presents a new method to measure the complexity and similarity of systems—cumulative Tsallis entropy based on the dispersion entropy (DCE). It is different from the traditional PE method to simply symbolize the sequence. Instead, the complexity of the system is characterized by focusing on the amplitude information of the time series and considering the influence of past events. We applied DCE to two kinds of simulation data and six global financial time series. The results show that DCE can be used as a diagnostic model to classify global financial data according to regional characteristics, financial background and government policies. In addition, as a classical method of non-stationary time series, we combine the MSE method with DCE to observe the financial market from different time scales and obtain rich intrinsic properties.

     

Bios data analyzer

The Bios Data Analyzer (BDA) is a set of computer programs (CD-ROM, in Sabelli et al., Bios. A Study of Creation, 2005) for new time series analyses that detects and measures creative phenomena, namely diversification, novelty, complexes, nonrandom complexity. We define a process as creative when its time series displays these properties. They are found in heartbeat interval series, the exemplar of bios .just as turbulence is the exemplar of chaos, in many other empirical series (galactic distributions, meteorological, economic and physiological series), in biotic series generated mathematically by the bipolar feedback, and in stochastic noise, but not in chaotic attractors. Differencing, consecutive recurrence and partial autocorrelation indicate nonrandom causation, thereby distinguishing chaos and bios from random and random walk. Embedding plots distinguish causal creative processes (e.g. bios) that include both simple and complex components of variation from stochastic processes (e.g. Brownian noise) that include only complex components, and from chaotic processes that decay from order to randomness as the number of dimensions is increased. Varying bin and dimensionality show that entropy measures symmetry and variety, and that complexity is associated with asymmetry. Trigonometric transformations measure coexisting opposites in time series and demonstrate bipolar, partial, and uncorrelated opposites in empirical processes and bios, supporting the hypothesis that bios is generated by bipolar feedback, a concept which is at variance with standard concepts of polar and complementary opposites.     

Intermittent observer for nonlinear systems with state delays

Kolmogorov–Sinai entropy-based irregularity measures such as approximate entropy (ApEn), sample entropy and fuzzy entropy are widely used for short-term heart rate variability analysis. These entropy statistics are estimated for a specific value of the tolerance parameter (r) that is mostly chosen from a common recommended range. Entropy measurement on short-term signals is highly sensitive to the choice of r. An incorrect selection of r results in an inaccurate entropy value, thereby leading to unreliable information retrieval. By addressing this inaccuracy due to r selection, the quality and reliability of information retrieval can be improved. Thus, we hypothesize that generating a complete entropy profile using all potential r values will give a more complete and useful information about signal irregularity in contrast to the case of finding entropy at a single selected value of r. In order to do so, one must be able to accurately select all potential r candidates. In this paper, we use a data-driven algorithm based on cumulative histograms to automatically select potential r values for an individual signal based on its dynamics. An appropriate set of r values is designated by the algorithm for generating a series of ApEn values (ApEn profile) instead of a single value of ApEn. ApEn profile- based secondary measures such as TotalApEn and SDApEn have been used as features to classify sets of synthetic and physiologic data. Our study proves that secondary measures obtained from an ApEn profile are more efficient in indicating irregularity levels in comparison with the traditional measure of ApEn evaluated at a single r value, specially in the case of short length data.     

Compressible Euler Equations¶with General Pressure Law

We study the hyperbolic system of Euler equations for an isentropic, compressible fluid governed by a general pressure law. The existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new Euler-Poisson-Darboux equation, which is highly singular when the density of the fluid vanishes. New properties of cancellation of singularities in combinations of the entropy kernel and the associated entropy-flux kernel are found. We prove the strong compactness of any sequence that is uniformly bounded in L ^∞ and whose corresponding sequence of weak entropy dissipation measures is locally H ^-1 compact. The existence and large-time behavior of L ^∞ entropy solutions of the Cauchy problem are established. This is based on a reduction theorem for Young measures, whose proof is new even for the polytropic perfect gas. The existence result also extends to the p-system of fluid dynamics in Lagrangian coordinates. Accepted: December 16, 1999     

Second law analysis and optimization for film-wise condensation from downward flowing vapors onto a sphere

The present study performs entropy generation analysis and optimization for saturated vapor flowing slowly onto and condensed on an isothermal sphere. This analysis makes us understand the function of the entropy generation and optimization in film-wise condensation outside a sphere. The result demonstrates that entropy generation increases with both group Rayleigh and Brinkman numbers. The minimum entropy generation number in condensation heat transfer for optimal diameter (D) or optimal (Ra/Ja) is expressed in terms of the group Brinkman number. The result provides an immediate estimate of the relative increase in irreversibility associated with using a sphere of diameter (D) ≠ optimal diameter (D).     

Studies of Mental “Noise”

Successive tests of subjects' performance in reaction time tasks were treated as time series and submitted to spectrum analysis. Rather than revealing the white noise expected by the view that variability is due to random error (equivalent power across frequency), the power spectra revealed colored noise. The slopes of the power spectra did not vary much for tasks differing in memory requirements. Spectrum analysis of time series from the logistic map also showed colored noise in regions on the edge of chaos, showing that the presence of colored noise in cognitive data need not oblige a theoretical account based on a complex, high-dimensional, system.     

Noise Stimuli Improve the Accuracy of Target Aiming: Possible Involvement of Noise-Enhanced Balance Control

Balance stability is important for human beings. Previous studies have shown that mechanical noise applied to the soles of the feet via vibrating insoles can improve human balance control. In this study we designed an experimental procedure called standard aiming target test to quantitatively evaluate the effect of vibrating insole on specific task of aiming during standing. Ten subjects were asked to aim at a target sheet using laser gun, and the traces of their aimed light spots and the center of pressure (COP) were recorded simultaneously. The same test was repeated twice for each individual with vibrating insole off and on, respectively. To assess dynamic patterns in aiming spot and COP signals, we calculated the entropies in the magnitude increments of both signals at different time scales, i.e., multiscale entropies (MSE).We found that the vibrating insole significantly improved the aiming performance and led to increased entropy in the fluctuations of aiming spot displacement over a range of time scales from 0.001 to 0.05 s. In addition, subjects with larger entropies in the aiming spot fluctuations had better aiming performances. Furthermore, we found that the entropy of the light spot signal was positively correlated with the entropy of the magnitude time series of COP fluctuations. These results suggest that vibrating insoles is beneficial for the complex postural control process during target aiming, possibly via their dynamic influences on the balance regulatory system.     

Creativity as Information: Measuring Aesthetic Attractions

The linear and binary assumptions of information theory are compared to assumptions of nonlinear approaches to understanding human information transfer. A model of information in open systems that rely on qualitative and aesthetic assessments is proposed that includes elements of entropy dissipation. A mathematical definition of creativity is derived from the model. Reanalysis of an existing data set is used to show the effectiveness of the creativity algorithm.     

Universal Systems for Entropy Intervals

A topological system is universal for a class of ergodic measure-theoretic systems if its simplex of invariant measures contains, up to an isomorphism, all elements of this class and no elements from outside the class. We construct universal systems for classes given by the combination of three properties: measure-theoretic entropy belonging to a nondegenerate interval of the extended nonnegative real halfline, invertibility and aperiodicity. For classes consisting of aperiodic systems the universal system can be made minimal.     

Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria

We study, globally in time, the velocity distribution f(v,t) of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field E. The density f satisfies a Boltzmann-type kinetic equation containing a fully nonlinear electron‐electron collision term as well as linear terms representing collisions with reservoir particles having a specified Maxwellian distribution. We show that when the constant in front of the nonlinear collision kernel, thought of as a scaling parameter, is sufficiently strong, then the L ¹ distance between f and a certain time-dependent Maxwellian stays small uniformly in t. Moreover, the mean and variance of this time‐dependent Maxwellian satisfy a coupled set of nonlinear ordinary differential equations that constitute the “hydrodynamical” equations for this kinetic system. This remains true even when these ordinary differential equations have non‐unique equilibria, thus proving the existence of multiple stable stationary solutions for the full kinetic model. Our approach relies on scale‐independent estimates for the kinetic equation, and entropy production estimates. The novel aspects of this approach may be useful in other problems concerning the relation between the kinetic and hydrodynamic scales globally in time. (Accepted September 3, 1996)     

Dynamics of a physical SBT memristor-based Wien-bridge circuit

The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article, we present two new coarse-grained estimators for the correlation dimension and for the correlation entropy. They can be easily estimated from the calculation of two U-correlation integrals. We have also developed an algorithm that is able to automatically obtain these invariants and the noise level in order to process large data sets. This method has been statistically tested through simulations in low-dimensional systems. The results show that it is robust in presence of noise and short data lengths. In comparison with similar approaches, our algorithm outperforms the estimation of the correlation entropy.     

Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case

We present convergence results for an adaptive algorithm to compute free energies, namely the adaptive biasing force (ABF) method (Darve and Pohorille in J Chem Phys 115(20):9169–9183, 2001; Hénin and Chipot in J Chem Phys 121:2904, 2004). The free energy is the effective potential associated to a so-called reaction coordinate ξ(q), where q = (q ₁, … , q _3N ) is the position vector of an N-particle system. Computing free energy differences remains an important challenge in molecular dynamics due to the presence of metastable regions in the potential energy surface. The ABF method uses an on-the-fly estimate of the free energy to bias dynamics and overcome metastability. Using entropy arguments and logarithmic Sobolev inequalities, previous results have shown that the rate of convergence of the ABF method is limited by the metastable features of the canonical measures conditioned to being at fixed values of ξ (Lelièvre et al. in Nonlinearity 21(6):1155–1181, 2008). In this paper, we present an improvement on the existing results in the presence of such metastabilities, which is a generic case encountered in practice. More precisely, we study the so-called bi-channel case, where two channels along the reaction coordinate direction exist between an initial and final state, the channels being separated from each other by a region of very low probability. With hypotheses made on ‘channel-dependent’ conditional measures, we show on a bi-channel model, which we introduce, that the convergence of the ABF method is, in fact, not limited by metastabilities in directions orthogonal to ξ under two crucial assumptions: (i) exchange between the two channels is possible for some values of ξ and (ii) the free energy is a good bias in each channel. This theoretical result supports recent numerical experiments (Minoukadeh et al. in J Chem Theory Comput 6:1008–1017, 2010), where the efficiency of the ABF approach is demonstrated for such a multiple-channel situation.     

Mathematical foundation of a new complexity measure

For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.     

光纤陀螺零偏稳定性的数据建模方法研究

光纤陀螺零偏稳定性是非系统性的随机变化漂移率,在惯性系统中不能用简单的方法加以补偿,因而其成为衡量光纤陀螺精度的重要指标。但通过时间序列分析中的数据建模方法可对光纤陀螺的零漂测试数据建立零偏稳定性数学模型。这样,在由光纤陀螺构成的惯性系统中利用卡尔曼滤波方法可使光纤陀零稳定性对系统精度的影响降至最低限度。中还对建模过程作了较详细的阐述。