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Michael Small

Publications and source records attributed to Michael Small.

14 recordsLinked to original sources

Testing for correlation structures in short-term variabilities with long-term trends of multivariate time series.

We describe a method for identifying correlation structures in irregular fluctuations (short-term variabilities) of multivariate time series, even if they exhibit long-term trends. This method is based on the previously proposed small shuffle surrogate method. The null hypothesis addressed by this method is that there is no short-term correlation structure among data or that the irregular fluctuations are independent. The method is demonstrated for numerical data generated by known systems and applied to several experimental time series.

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Testing for nonlinearity in irregular fluctuations with long-term trends.

We describe a method for investigating nonlinearity in irregular fluctuations (short-term variability) of time series even if the data exhibit long-term trends (periodicities). Such situations are theoretically incompatible with the assumption of previously proposed methods. The null hypothesis addressed by our algorithm is that irregular fluctuations are generated by a stationary linear system. The method is demonstrated for numerical data generated by known systems and applied to several actual time series.

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Small-shuffle surrogate data: testing for dynamics in fluctuating data with trends.

We describe a method for identifying dynamics in irregular time series (short term variability). The method we propose focuses attention on the flow of information in the data. We can apply the method even for irregular fluctuations which exhibit long term trends (periodicities): situations in which previously proposed surrogate methods would give erroneous results. The null hypothesis addressed by our algorithm is that irregular fluctuations are independently distributed random variables (in other words, there is no short term dynamics). The method is demonstrated for numerical data generated by known systems, and applied to several actual time series.

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Testing for nonlinearity in time series without the Fourier transform.

A method to test for nonlinearity in time series, without the need to apply the Fourier transform, is proposed. This method therefore avoids the drawbacks of previously proposed surrogate techniques associated with the estimation of the signal's power spectrum. The test addressed by this algorithm is that the data are generated by a stationary linear system. To achieve this, the algorithm takes advantage of the fundamentally different structure of linear and nonlinear systems.

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Optimal phase-space projection for noise reduction.

In this communication we will reexamine the widely studied technique of phase-space projection. By imposing a time-domain constraint on the residual noise, we deduce a more general version of the optimal projector, which includes those appearing in previous literature as subcases but does not assume the independence between the clean signal and the noise. As an application, we will apply this technique for noise reduction. Numerical results show that our algorithm has succeeded in augmenting the signal-to-noise ratio for simulated data from the Rössler system and experimental speech record.

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Scale-free user-network approach to telephone network traffic analysis.

The effect of the user network on the telephone network traffic is studied in this paper. Unlike classical traffic analysis, where users are assumed to be connected uniformly, our proposed method employs a scale-free network to model the behavior of telephone users. Each user has a fixed set of acquaintances with whom the user may communicate, and the number of acquaintances follows a power-law distribution. We show that compared to conventional analysis based upon a fully connected user network, the network traffic is significantly different when the user network assumes a scale-free property. Specifically, network blocking (call failure) is generally more severe in the case of a scale-free user network. It is also shown that the carried traffic is practically limited by the scale-free property of the user network, rather than by the network capacity.

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Surrogate test to distinguish between chaotic and pseudoperiodic time series.

In this paper a different algorithm is proposed to produce surrogates for pseudoperiodic time series. By imposing a few constraints on the noise components of pseudoperiodic data sets, we devise an effective method to generate surrogates. Unlike other algorithms, this method properly copes with pseudoperiodic orbits contaminated with linear colored observational noise. We will demonstrate the ability of this algorithm to distinguish chaotic orbits from pseudoperiodic orbits through simulation data sets from the Rössler system. As an example of application of this algorithm, we will also employ it to investigate a human electrocardiogram record.

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Equivalence between "feeling the pulse" on the human wrist and the pulse pressure wave at fingertip.

Feeling the pulse on the wrist is the regular diagnostic method in traditional Chinese medicine. However it is natural to ask whether there is any difference between feeling the pulse on the wrist or at any other part of the body: such as the fingertips at which it is easily measured by electronic devices. We employ a series of neural networks to model blood pressure propagation from the wrist to the fingertip. In order to avoid the problem of over-fitting we apply information theoretic criterion to determine the optimal model in these networks and then apply surrogate data method to the residuals in this model. We demonstrate the application of this method to recordings of human pulse in six subjects. Our result indicates that there is no significant difference between pulse waveform measure on the lateral arterial artery (wrist) and at the fingertip.

Blood Pressure↗

Enzyme blockade: a nonradioactive method to determine the absolute rate of cholesterol synthesis in the brain.

The standard in vivo method to determine rates of brain cholesterol synthesis involves systemic injection of (3)H(2)O and measurement of incorporated radioactivity in sterols. Herein, we describe an alternative method ("enzyme blockade") that obviates the use of radioactivity. The method relies on the ability of AY9944, a potent and relatively selective inhibitor of cholesterol synthesis, to cause the time-dependent accumulation of 7-dehydrocholesterol (DHC), a cholesterol precursor detected with sensitivity and specificity by reverse-phase HPLC-coupled spectrophotometry at 282 nm. To validate the method, adult AY9944-treated and control mice were injected with [(3)H]acetate. After 24 h, most of the radioactivity in brain sterols from treated mice accumulated in DHC, without significantly perturbing overall sterol pathway activity, compared with controls (where cholesterol was the dominant radiolabeled sterol, with no label found in DHC). When adult mice were treated continuously with AY9944, the time-dependent accumulation of DHC in brain was linear (after approximately 8 h) for 3 days. The rate of brain cholesterol synthesis determined by this method ( approximately 30 microg/g/day) closely agrees with that determined by the radioactive method. We also determined the cholesterol synthesis rate in different regions of adult mouse brain, with frontal cortex having the highest rate and cerebellum having the lowest rate.

Animals↗

Effects of low-dose continuous combined HRT on vascular function in women with type 2 diabetes.

BACKGROUND: Improvement in vascular endothelial function is widley cited as a beneficial effect of hormone replacement therapy (HRT). Women with type 2 diabetes (T2DM) are at increased cardiovascular risk and have impaired endothelial function. Any benefits of HRT on endothelial function in this group are of particular interest. OBJECTIVES: We assessed effects on vascular function of oral 17beta oestradiol (1 mg) and norethisterone (0.5 mg) in postmenopausal women with T2DM. DESIGN: Double-blind, randomised, placebo-controlled trial. ASSESSMENTS: Twenty-eight women had pulse wave velocity (PWV) and adhesion molecules VCAM-1 and ICAM-1 assessed before and after three months' treatment. Twenty-four women also had gluteal fat biopsy for assessment of resistance vessel function (using wire myography). RESULTS: HRT did not affect PWV, VCAM-1, ICAM-1 or carbachol response. Effects of L-NAME and indomethacin on carbachol sensitivity were similar in both groups. CONCLUSIONS: This HRT preparation had no detectable effect on these measures of endothelial function in women with T2DM.

Arteries↗

Clinical impact of the new criteria for the diagnosis of diabetes mellitus.

In 1997 the American Diabetes Association lowered the threshold for diagnosis of diabetes from a fasting plasma glucose concentration of 7.8 mmol/l to 7.0 mmol/l and advised that the oral glucose tolerance test no longer be used in routine clinical practice. In 1999 the World Health Organization endorsed the reduction in fasting plasma glucose threshold but recommended retaining the oral glucose tolerance test for anyone with impaired fasting glucose (6.1 mmol/l-6.9 mmol/l). This Review discusses the impact of these changes on the prevalence of diabetes and examines the implications for individuals and specific high-risk groups. The phenotype of those diagnosed with diabetes and the predictive value for the development of complications according to the different criteria are compared. It is clear that these changes in diagnostic criteria have major importance both for individuals and for resource planning at a national level.

Diabetes Complications↗

Minimum description length neural networks for time series prediction.

Artificial neural networks (ANN) are typically composed of a large number of nonlinear functions (neurons) each with several linear and nonlinear parameters that are fitted to data through a computationally intensive training process. Longer training results in a closer fit to the data, but excessive training will lead to overfitting. We propose an alternative scheme that has previously been described for radial basis functions (RBF). We show that fundamental differences between ANN and RBF make application of this scheme to ANN nontrivial. Under this scheme, the training process is replaced by an optimal fitting routine, and overfitting is avoided by controlling the number of neurons in the network. We show that for time series modeling and prediction, this procedure leads to small models (few neurons) that mimic the underlying dynamics of the system well and do not overfit the data. We apply this algorithm to several computational and real systems including chaotic differential equations, the annual sunspot count, and experimental data obtained from a chaotic laser. Our experiments indicate that the structural differences between ANN and RBF make ANN particularly well suited to modeling chaotic time series data.

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Modeling continuous processes from data.

Experimental and simulated time series are necessarily discretized in time. However, many real and artificial systems are more naturally modeled as continuous-time systems. This paper reviews the major techniques employed to estimate a continuous vector field from a finite discrete time series. We compare the performance of various methods on experimental and artificial time series and explore the connection between continuous (differential) and discrete (difference equation) systems. As part of this process we propose improvements to existing techniques. Our results demonstrate that the continuous-time dynamics of many noisy data sets can be simulated more accurately by modeling the one-step prediction map than by modeling the vector field. We also show that radial basis models provide superior results to global polynomial models.

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Deterministic nonlinearity in ventricular fibrillation.

We provide numerical evidence that the electrocardiogram data collected from pigs during induced ventricular fibrillation cannot be described by a monotonic nonlinear transformation of linearly filtered noise. To establish this we use surrogate techniques and apply two test statistics: (1) the Takens' maximum likelihood estimator of the Grassberger-Procaccia correlation dimension and (2) an improved correlation dimension estimation routine. The improved dimension estimates provide evidence that the correlation dimension of the underlying dynamics during the episode of VF in the first 30 s is slightly less than 6. This result is consistent and reproducible among subjects. (c) 2000 American Institute of Physics.

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