Search results for "Exponent"
showing 10 items of 896 documents
Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent
1995
The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. Du…
Benefits of nonlinear analysis indices of walking stride interval in the evaluation of neurodegenerative diseases.
2021
Indices characterising the long-range temporal structure of walking stride interval (SI) variability such as Hurst exponent (H) and fractal dimension (D) may be used in addition to indices measuring the amount of variability like the coefficient of variation (CV). We assess the added value of the former indices in a clinical neurological context. Our aim is to demonstrate that they provide a clinical significance in aging and in frequent neurodegenerative diseases such as Parkinson's disease, Huntington, and amyotrophic lateral sclerosis. Indices assessing the temporal structure of variability are mainly dependent on SI time series length and algorithms used, making quantitative comparisons…
Nonlinear analysis of sleep eeg in depression: Calculation of the largest lyapunov exponent
1995
Conventional sleep analysis according to Rechtschaffen and Kales (1968) has provided meaningful contributions to the understanding of disturbed sleep architecture in depression. However, there is no characteristic alteration of the sleep cycle, which could serve as a highly specific feature for depressive illness. Therefore, we started to investigate nonlinear properties of sleep electroencephalographic (EEG) data in order to elucidate functional alterations other than those obtained from classical sleep analysis. The application of methods from nonlinear dynamical system theory to EEG data has led to the assumption that the EEG can be treated as a deterministic chaotic process. Chaotic sys…
Unique sleep-stage transitions determined by obstructive sleep apnea severity, age and gender
2019
In obstructive sleep apnea, patients' sleep is fragmented leading to excessive daytime sleepiness and co-morbidities like arterial hypertension. However, traditional metrics are not always directly correlated with daytime sleepiness, and the association between traditional sleep quality metrics like sleep duration and arterial hypertension is still ambiguous. In a development cohort, we analysed hypnograms from mild (n = 213), moderate (n = 235) and severe (n = 277) obstructive sleep apnea patients as well as healthy controls (n = 105) from the European Sleep Apnea Database. We assessed sleep by the analysis of two-step transitions depending on obstructive sleep apnea severity and anthropom…
Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.
2015
We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher or…
Influence of Duration of Experiment on Rate of Uptake of Radioactive Potassium in Smooth Muscle
1963
THE rates of uptake and loss of radioactive tracers by excitable tissues can often be described by a function involving one exponential term1–3, but over relatively long periods deviations have been observed from such a simple course4–7. The rates of exchange towards the end of such periods are commonly slower than would be predicted from the initial rates and two general causes for this behaviour have been suggested: either the rates are, in fact, diminishing during the course of an experiment or the tissue is not behaving uniformly. This latter possibility has been extensively investigated1,8–15, because biological material shows an obvious lack of uniformity, and because deviations from …
On the critical behavior for time-fractional pseudo-parabolic type equations with combined nonlinearities
2022
AbstractWe are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form $|u|^{p}+\iota |\nabla u|^{q}$ | u | p + ι | ∇ u | q , where $p,q>1$ p , q > 1 , and $\iota \geq 0$ ι ≥ 0 is a constant. The cases $\iota =0$ ι = 0 and $\iota >0$ ι > 0 are discussed separately. For each case, the critical exponent in the Fujita sense is obtained. We point out two interesting phenomena. First, the obtained critical exponents are independent of the fractional orders of the time derivative. Secondly, in the case $\iota >0$ ι > 0 , we show that the gradie…
Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations
2005
We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.
Influence of the electro-optical properties of an a-Si:H single layer on the performances of a pin solar cell
2012
We analyze the results of an extensive characterization study involving electrical and optical measurements carried out on hydrogenated amorphous silicon (α-Si:H) thin film materials fabricated under a wide range of deposition conditions. By adjusting the synthesis parameters, we evidenced how conductivity, activation energy, electrical transport and optical absorption of an α-Si:H layer can be modified and optimized. We analyzed the activation energy and the pre-exponential factor of the dark conductivity by varying the dopant-to-silane gas flow ratio. Optical measurements allowed to extract the absorption spectra and the optical bandgap. Additionally, we report on the temperature dependen…
The kinetic behavior of insulin fibrillation is determined by heterogeneous nucleation pathways
2005
When subjected to acidic conditions and high temperature, insulin is known to produce fibrils that display the common properties of disease amyloids. Thus, clarifying the mechanisms of insulin fibrillation can help the general understanding of amyloidal aggregation. Insulin fibrillation exhibits a very sharp time dependence, with a pronounced lag phase and subsequent explosive growth of amyloidal aggregates. Here we show that the initial stages of this process can be well described by exponential growth of the fibrillated proteins. This indicates that the process is mainly controlled by a secondary nucleation pathway.