Using the modified sample entropy to detect determinism

A modified sample entropy (mSampEn), based on the nonlinear continuous and convex function, has been proposed and proven to be superior to the standard sample entropy (SampEn) in several aspects. In this Letter, we empirically investigate the ability of the mSampEn statistic combined with surrogate data method to detect determinism. The effects of the datasets length and noise on the proposed method to differentiate between deterministic and stochastic dynamics are tested on several benchmark time series. The noise performance of the mSampEn statistic is also compared with the singular value decomposition (SVD) and symplectic geometry spectrum (SGS) based methods. The results indicate that the mSampEn statistic is a robust index for detecting determinism in short and noisy time series.     

一种新的时间序列确定性辨识方法

提出一种新的基于辛几何谱的时间序列确定性检测方法，通过计算原始时间序列及其替代数据的辛几何谱，利用非参数Mann-Whitney 秩和检验方法，可有效地辨别确定性混沌过程和随机过程.通过对常见的随机过程，Lorenz，Rssler，Mackey-Glass，高维耦合方程的仿真检验，说明了方法的有效性. 并通过用Santa Fe测试集中两个序列检验了其对实际时间序列的适用性，最后研究不同数据长度和不同强度噪声对该方法性能的影响说明了其鲁棒性.     

一种时间序列的弱非线性检验方法

时间序列的非线性是判定该时间序列具有混沌特性的必要条件.提出一种基于线性和非线性AR模型归一化多步预测误差比值的非线性检验量δ_NAR,采用替代数据法来检测时间序列中的弱非线性.以Lorenz时间序列为例,分析了估计非线性检验量δ_NAR时各相关参数对弱非线性检测性能的影响.通过混沌时间序列非线性检测试验,对4种混沌时间序列中的3种,非线性检验量δ_NAR都表现出比基于AIC模型选择准则的非线性检验量相似文献   

The effect of time delay on Approximate & Sample Entropy calculations

Approximate and Sample Entropy are two widely used techniques to measure system complexity or regularity based on chosen parameters such as pattern length, m, and tolerance, r. In this paper, we investigate how different values of the time delay parameter, τ can be used in conjunction with standard values of m and r in the computation of Approximate and Sample Entropy. The results show that for time series generated by nonlinear dynamics that have long range correlation, a time delay equal to the first zero crossing or minimum of the autocorrelation function can provide additional information into the characteristics of the time series that may be useful in comparative analysis. With a unity delay, we demonstrate that Approximate and Sample Entropy are possibly measuring only the (linear) autocorrelation properties of the signal, and these are highly invariant under surrogate data generation methods. Hence when this occurs, the complexity measures of the surrogate and original data are not statistically different.     

Characterization of complex behaviors of TCP/RED computer networks based on nonlinear time series analysis methods

Packet-level observations are representative of the high sensitivity of TCP/RED computer network behavior with respect to network/RED parameter variations. That is, while we do not have any control on network parameters, mis-choosing of the RED parameters results in complex non-periodic oscillations in the router queue length that may damage the Quality of Service requirements. Characterizing the nature of such behaviors, however, helps the network designers to modify the RED design method in order to achieve better overall performance. In this paper, we first investigate the effect of variations in different RED parameters on the network behavior and then seek for the origin of such complex behaviors. For this purpose, different linear and nonlinear time series analysis methods have been applied to long-duration ns-2 packet-level data traces of a homogeneous TCP/RED network. The results of the analysis confirm that the complex behavior of the network can be represented by a nonlinear stochastic second-order process and it is not due to a deterministic chaos or a non-stationarity in the network.     

连续动力系统时间序列的非线性检验

用相位随机化的替代数据方法，研究了连续混沌动力系统时间序列的非线性检验判定.研究发现，在不同的采样情况下，混沌时间序列的非线性特性检验有所差异，尤其对于过采样时间序列，往往会出现虚假的判断结果.针对过采样时间序列，最好采用能够反映非线性特征的参数，作为检验统计量进行检验判断. 关键词： 替代数据 关联维数 连续时间序列 非线性检验     

Recovery of delay time from time series based on the nearest neighbor method

We propose a method for the recovery of delay time from time series of time-delay systems. The method is based on the nearest neighbor analysis. The method allows one to reconstruct delays in various classes of time-delay systems including systems of high order, systems with several coexisting delays, and nonscalar time-delay systems. It can be applied to time series heavily corrupted by additive and dynamical noise.     

The application of proton nuclear magnetic resonance imaging for the in vivo characterisation of chemically induced renal lesions in rats over a prolonged time study

Renal cortical and medullary spin-lattice (T₁) relaxation times were measured at various time points over a period of 56 days following the administration of a single i.p. injection of 100 mg/kg 2-bromoethanamine hydrobromide (BEA), 200 mg/kg hexachloro-1,3-butadiene (HCBD) or 100 mg/kg puromycin aminonucleoside (PAN) to male Wistar rats. Administration of a single injection of HCBD caused a dramatic, immediate rise in the cortical T₁ values above control values, and these levels remained elevated until, by Day 28 postinjection the levels were back to control values. Administration of BEA also caused an elevation in cortical T₁ values, but in this case these values remained above control values for the rest of the study. The administration of PAN did not produce any significant increases in cortical T₁ values until 14 days postinjection. The elevated T₁ values remained above control values for the rest of the study. These increases observed in cortical T₁ values appeared to be mirrored by decreases in medullary T₁ values. Increases in cortical T₁ values were accompanied by visual changes in the NMR images and enlargement of the kidneys. The histological findings were consistent with the NMR data, confirming that morphologically the tissues did show a full recovery by Day 28 in the HCBD-treated animals. This was not the case following injection of both BEA and PAN, where necrosis was not reversible and there was no recovery of the tissues.     

Novel method for measurement of retardance of a quarter-wave plate

A novel and simple method used for measurement of retardance of a quarter-wave plate employing two polaroids and a right-angle prism is reported. The theoretical analysis of the principle is given taking the Jones matrix as a mathematical tool. The uncertainty of the method is theoretically analyzed. An application example is also given. The measured result of the example is verified with a test. The main advantage of this method is that it can completely determine the retardance value, which overcomes the shortcomings of the existing methods reported before for determining only the multi-value function values, such as cosine or tangent value of the retardance. In addition, this method is also accurate, easy to operate and can also be used for the retardance measurement of other retardation plates.     

Transport measurements through stacked InAs self-assembled quantum dots in time domain

We report electronic characterization of stacked InAs self-assembled quantum dots (SAQDs) embedded in GaAs, using ultra-short pulses. Electrical pulse trains with the width ranging from 50 to 500 ps were applied on the waveguide-type top electrode and the average substrate current was monitored. The current showed staircases and oscillatory features as a function of the pulse width. The staircase could represent single electron injection into SAQDs and the observed oscillatory features could be related with temporal change of electronic occupation in quantum states of SAQDs.     

Myocardial proton spin-lattice relaxation times in vitro: Effect of elapsed time after excision

An assumption made in using excised tissue for in vitro nuclear magnetic resonance (NMR) studies is that variables of interest, such as spin-lattice (T₁) relaxation times, remain stable for periods of time after excision sufficient to perform NMR spectroscopy. In this study, we evaluated the changes in T₁ of rat myocardium, measured at two NMR field strengths, at serial time intervals up to 72 hours postmortem. Left ventricular myocardium from six male Sprague-Dawley rats was excised and stored at room temperature in sealed NMR sample tubes. Spin-lattice relaxation times were determined with a modified inversion-recovery pulse sequence immediately postmortem and at intervals up to 72 hours post-excision; NMR studies were performed using 90 MHz and 360 MHz spectrometers. A gradual decrease in T₁ was noted with increasing time post-excision; T₁ was not significantly shorter than baseline until 72 hours postmortem at either field strength. The rate of change of T₁ was similar at the two field strengths. At any given time post-excision, T₁ was significantly higher (p < 0.001) at 360 MHz than at 90 MHz. We conclude that, with proper tissue handling and storage techniques, rat myocardial T₁ is stable postmortem sufficiently long to permit meaningful NMR studies of excised tissue.     

Equal heartbeat intervals and their effects on the nonlinearity of permutation-based time irreversibility in heart rate

The association of equal heartbeat intervals with cardiac conditions and the effect of the equality on permutation-based time irreversibility are investigated in this paper. We measure the distributions of equal heartbeat intervals under three conditions, namely congestive heart failure (CHF), healthy young and elderly, whose time irreversibility is detected by measuring the probabilistic difference between permutations instead of raw vectors. We demonstrate that heartbeats contain high rates of equal states, particularly the CHF with around 20% equalities, and the distributions of equal values discriminate the heartbeats at very short data length. The CHF have more equal values than the healthy young (p $<1.47?{10}^{?15}$) and elderly (p $<2.48?{10}^{?11}$), and the healthy young have less equalities than the elderly (p $<3.16?{10}^{?4}$). Time irreversibility considering equal values is promising to extract nonlinear behaviors of heartbeats, confirming the decreased nonlinear complexity of the diseased and aging heart rates, while that involving no equality leads to erroneous nonlinearity detection. In our contribution, we highlight the pathological or physiological information contained by the distribution of equal heartbeat intervals that might contribute to develop relevant biomarkers in the area of heart analysis, and demonstrate the effectiveness of equality-based time irreversibility in the nonlinearity detection of heartbeats.     

Lactate observation in vivo by spectral editing in real time

We have developed a novel in vivo proton MR spectroscopy magnetization transfer method for detection of lactate in ischemic tissue in the presence of interfering fat proton resonances. Pyruvate is magnetically labeled with a saturation pulse and, when converted to lactate, the lactate retains the label. Difference of spectra obtained with and without a saturation pulse contain no fat resonances. High-resolution spectra (determined with a GE 1.5 T Signa) of low lactate levels were obtained in vivo by water suppression using a 2662 composite RF pulse and slice-selective gradients. Spectral subtraction was performed in real time allowing the monitoring of a buildup of the intensity of the lactate peak. Pyruvate-lactate saturation transfer techniques should find wide applicability in the study of ischemia.     

Detection of determinism and randomness in time series: A method based on phase space overlap of attractors

The space overlap of an attractor reconstructed from a time series with a similarly reconstructed attractor from a random series is shown to be a sensitive measure of determinism. Results for the time series for Henon, Lorenz and Rössler systems as well as a linear stochastic signal and an experimental ECG signal are reported. The overlap increases with increasing levels of added noise, as shown in the case of Henon attractor. Further, the overlap is shown to decrease as noise is reduced in the case of the ECG signal when subjected to singular value decomposition. The scaling behaviour of the overlap with bin size affords a reliable estimate of the fractal dimension of the attractor even with limited data.     

Investigations of backscattering peaks and of the nature of the confining potential in open quantum dots

The properties of open quantum dots are examined in magneto-transport. The quantum dots are prepared from a two-dimensional electron system (2DES) in AlGaAs/GaAs by lateral gate structures. These quantum dots are open, i.e. they are still connected to the surrounding 2DES regions. The low magnetic field magnetoresistance shows peak structures. These structures can be related to semi-classical ballistic trajectories in the confining potential of a dot. The calculations of different confining potentials (abrupt “hard-wall” and parabolic “soft-wall”) are compared with the experimental results. The experiments are better described by a soft-wall potential.     

Increasing the yield from volumetric MRI in patients with epilepsy

Volumetric magnetic resonance imaging has become a routine investigation in the management of patients with chronic partial epilepsy. However, even with the use of reformatted images, an underlying cause for epileps can-not be found in many of these patients. We show that further processing of the data, including three-dimensional reconstruction and quantitative analysis of the volume and complexity of the images in three dimensions, reveals additional positive information in up to 75% of patients. This may be useful for surgical planning, prognostication, and understanding of the structure and development of the human brain.     

An assessment of the safety of rapidly changing magnetic fields in the rabbit: Implications for NMR imaging

The effects of rapidly changing magnetic fields on the cardiac and respiratory functions of anaesthetised rabbits have been investigated. No changes were observed using pulsed fields with peak rates of change of 60 T/sec. The implications of these experiments for the safety of NMR imaging are discussed.     

A rotating phantom for the study of flow effects in MR imaging

A common type of phantom used for the study of flow effects in MR imaging is the tube phantom, where a liquid passes through a set of tubes placed in the main magnetic field of an MR scanner. Among the disadvantages with this type of phantom are that a distribution of velocities is present in each tube, and that quantifications of flow effects using tube phantoms may be very time-consuming. In this work, we describe the design and the properties of a rotating wheel flow phantom used for quantification of the effects of flow through the imaging plane as well as in the imaging plane. The proposed phantom is constructed as a rotating gel-filled wheel, surrounded by static volumes filled with the same gel, and the evaluation of the information from rotating and static parts is made with a specially designed computer program. The phantom can be used as a plug flow phantom covering simultaneously an interchangeable velocity interval, which at present has the range −52 mm/s, +52 mm/s. It is shown that the phantom gives adequate information on the dependence of pixel content on first-order motion in MR modulus and phase images. Among the fields of application are rapid calibration of MR imaging units for flow determination using phase information, as well as testing of pulse sequence characteristics and verification of theoretical predictions concerning the flow dependence in MR images.     

Identification of patients with hereditary haemochromatosis by magnetic resonance imaging and spectroscopic relaxation time measurements

A total of 4302 healthy blood donors were screened for elevated serum ferritin and transferrin saturation. Fifteen had increased serum ferritin at a follow-up examination. Five relatives of these donors also entered the study. Eleven patients had elevated liver iron concentrations, while five had normal liver iron concentrations. The R₂ relaxation rate in the liver was first measured with a conventional multi-spin-echo imaging sequence, and then by a volume-selective spectroscopic multi-spin-echo sequence, in order to achieve a minimum echo time of 4 msec. No correlation was found between the relaxation rate R₂ and the liver iron concentration, when R₂ was calculated from the imaging data. Multi-exponential transverse relaxation could be resolved when the spectroscopic sequence was used. A strong correlation between the initial slope of the relaxation curve and the liver iron concentration was found (r = 0.90, p < 0.001). Signal intensity ratios between liver and muscle were calculated from the first three echoes in the multi-echo imaging sequence, and from a gradient echo sequence. A strong correlation between the logarithm of the signal intensity ratios and the liver iron concentration was found. Although both spectroscopic T₂ relaxation time measurements and signal intensity ratios could be used to quantify liver iron concentration, the gradient echo imaging seemed to be the best choice. Gradient echo imaging could be performed during a single breath hold, so motion artifacts could be avoided. The accuracy of liver iron concentration estimates from signal intensity ratios in the gradient echo images was about 35%.     

Effects of the dark-exciton state on photoluminescence dynamics in surface-modified CdS quantum dots prepared by a colloidal method

We have investigated exciton dynamics in surface-modified CdS quantum dots (QDs) prepared by a colloidal method. The size- and surface-controlled CdS QDs have been successfully prepared by using a size-selective photoetching and surface modification technique. The decay profiles exhibit an unusual temperature dependence: increase of the decay time with increase in temperature. The temperature dependence of the decay profiles can be explained in terms of a three-level model including the exciton state with a triplet origin, the so-called dark-exciton state.