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Results for “Gaussian process”

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PubMed1979

The response of a spatially distributed neuron to white noise current injection.

The depolarization of passive nerve cylinder or dendritic tree in the equivalent cylinder representation is assumed to satisfy the cable equation. We consider in detail the effects of white noise current injection at a given location for the case of sealed end boundary conditions and for an initial resting state. The depolarization at a point is a Gaussian random process but is not Markovian. Expression (infinite series) are obtained for the expectation, variance, spatial and temporal covariances of the depolarization. We examine the steady state expectation and variance and investigate how these are approached in time over the whole neuronal surface. We consider the relative contributions of various terms in the series for the expectation and variance of the depolarization at x = 0 (soma, trigger zone, recording electrode) for various positions of the input process. It is found that different numbers of terms must be taken to obtain a reasonable approximation depending on whether the stimulus is at proximal, central or distal parts of the dendritic tree. We consider briefly the interspike time problem and see in an approximate way how spatial effects are important in determining the mean time between impulses.

Action Potentials↗

PubMed1985

A maximum entropy criterion of filtering and coding for stationary autoregressive signals: its physical interpretations and suggestions for its application to neural information transmission.

The operations of encoding and decoding in communication agree with filtering operations of convolution and deconvolution for Gaussian signal processing. In an analogy with power transmission in thermodynamics, an autoregressive model of information transmission is proposed for representing a continuous communication system which requires a pair of an internal noise source and a signal source to encode or decode a message. In this model transinformation (informational entropy) equals the increase in stationary nonequilibrium organization formed through the amplification of white noise by a positive feedback system. The channel capacity is finite due to the existence of inherent noise in the system. The maximum entropy criterion in information dynamics corresponds to the 2nd law of thermodynamics. If the process is stationary, the communication system is invertible, and has the maximum efficiency of transformation. The total variation in informational entropy is zero in the cycle of the invertible system, while in the noninvertible system the entropy of decoding is less than that of encoding. A noisy autoregressive coding which maximizes transinformation is optimum, but is also ideal.

Animals↗

PubMed1993

Cardiac Doppler blood-flow signal analysis. Part 1. Evaluation of the normality and stationarity of the temporal signal.

The normality (Gaussian property) and stationarity of the cardiac Doppler blood-flow signal were evaluated on short-time segments distributed over the cardiac cycle. The basic approaches used to perform statistical tests on the nonstationary and quasiperiodic cardiac Doppler signal are presented. The results obtained from the data of ten patients having a normal aortic valve and ten patients having a stenotic valve indicate that a complex Gaussian random process is an acceptable approximation for the clinical cardiac Doppler signal. For segments of 10 ms or less, 82 per cent of them were accepted to be stationary with a significance level of 0.05, whereas for durations greater than 40 ms, the percentage of stationary segments was less than 75 per cent. It was concluded that the 10 ms window generally used in practice is a good choice for Doppler spectrogram estimation, but a shorter time interval would be preferable.

Aortic Valve↗

PubMedDate not supplied

Controlling behavioral experiments with a new programming language (SORCA) for microcomputer systems.

A new programming language SORCA has been defined and a compiler has been written for Z80-based microcomputer systems with CP/M operating system. The language was developed to control behavioral experiments by external stimuli and by time schedule in real-time. Eight binary hardware input lines are sampled cyclically by the computer and can be used to sense switches, level detectors and other binary information, while 8 binary hardware output lines, that are cyclically updated, can be used to control relays, lamps, generate tones or for other purposes. The typical reaction time (cycle time) of a SORCA-program is 500 microseconds to 1 ms. All functions can be programmed as often as necessary. Included are the basic logic functions, counters, timers, majority gates and other complex functions. Parameters can be given as constants or as a result of a step function or of a random process (with Gaussian or equal distribution). Several tasks can be performed simultaneously. In addition, results of an experiment (e.g., number of reactions or latencies) can be measured and printed out on request or automatically. The language is easy to learn and can also be used for many other control purposes.

Animals↗

PubMed1991

Assessing the variability of stochastic epidemics.

In predicting the course of individual realizations of an epidemic it is important to know the magnitude of the variability of such realizations about their mean. In this paper and in the context of the general stochastic epidemic, some methods of obtaining approximate estimates of this variability are investigated; one is a multivariate normal approximation based on an asymptotic Gaussian diffusion process, and another uses an approximating linear stochastic process. The extension of these methods to the more detailed models used to describe the transmission dynamics of HIV infection and AIDS is discussed.

Disease Outbreaks↗

PubMed1999

Correlation dimension of EEG slow-wave activity during sleep in narcoleptic patients under bed rest conditions.

The calculation of the correlation dimension (D2) was applied to the study of the profiles of EEG slow-wave activity in nine narcoleptic subjects and nine sex- and age-matched control subjects who, following a baseline night recording, were maintained on 16 h of diurnal sleep deprivation and, thereafter, submitted to a 32-h bed rest protocol. The reversibility test allowed us to reject the null hypothesis that the time series considered in our study were generated by a static transformation of a linear Gaussian random process. Similarly, all profiles showed a positive largest Lyapunov exponent. Finally, the computation of D2 showed an average value of 5.27 (0.68 S.D.) in normal controls and 4.05 (1.49 S.D.) in narcoleptic patients (p = 0.067). Four of the narcoleptic patients showed values of D2 lower than 4, this was never observed in the normal controls (p = 0.0294). This study indicates that the mechanism of sleep-wake regulation in narcolepsy shows a somewhat lower degree of complexity as compared to normal controls. In particular, these data seem to confirm the already suggested different and simpler coupling between the homeostatic process of sleep regulation and the circadian and ultradian drives to sleep that occurs in bed rest condition in this disease.

Adult↗

PubMed1999

Measuring the coherence of intracranial electroencephalograms.

OBJECTIVE: Previous coherence studies of human intracranial electroencephalograms (EEGs) can be faulted on two methodological issues: (1) coherence estimates in a majority were formed from a very small number of independent sample spectra, and (2) the statistical significance of coherence estimates was either not reported or was poorly evaluated. Coherence estimator performance may be poor when a small number of independent sample spectra are employed, and the coupling of poor estimation and statistical testing can result in inaccuracy in the measurement of coherence. The performance characteristics of the coherence estimator and statistical testing of coherence estimates are described in this manuscript. METHODS: The bias, variance, probability density functions, and confidence intervals of the estimate of magnitude squared coherence (MSC); and power analysis for the test of zero MSC were developed from the exact analytic form of the probability density function of the estimate of MSC for Gaussian random processes. The coherence of a single epoch of background EEG, recorded from a patient with intractable seizures, was evaluated with different parameter values to aid in the exposition of the concepts developed here. RESULTS: The statistical characteristics of WOSA coherence estimates are a function of a single estimator parameter, the number of independent sample spectra employed in the estimation. Bias and variance are high, confidence intervals may be large, and the probability of Type II errors is high if a small number of independent sample spectra are employed. A considerable improvement in measurement accuracy is possible with careful selection of estimator parameter values. CONCLUSIONS: Coherence measurement accuracy can be improved over previous applications by attention to estimator performance and accurate statistical testing of coherence estimates.

Adult↗

PubMed2000

The asymptotic distribution of canonical correlations and variates in cointegrated models.

The cointegrated model considered here is a nonstationary vector autoregressive process in which some linear functions are stationary and others are random walks. The first difference of the process (the "error-correction form") is stationary. Statistical inference, such as reduced rank regression estimation of the coefficients of the process and tests of hypotheses of dimensionality of the stationary part, involves the canonical correlations between the difference vector and the relevant vector of the past of the process. The asymptotic distributions of the canonical correlations and the canonical vectors under the assumption that the process is Gaussian are found.

Journal Article↗

PubMed1991

Synaptic noise and the cross-correlation between motoneuron discharges and stimuli.

Theoretical analysis of motoneuron models predicts that the cross-correlogram between motoneuron discharges and stimuli should reflect the derivative of the post-synaptic potential (PSP) in the absence of synaptic noise. The cross-correlogram peaks become wider if the amplitude of the noise is significant. To deal with this case, the linear combination of the PSP and its first derivative has been proposed as an approximation. The synaptic noise was regarded as a Gaussian stochastic process (its diffusion approximation), and the estimation of the cross-correlation function for this case is presented. The results were found to be in agreement with reported experimental data. A comparison was made with the linear combination approximation and with the reported computer simulation.

Animals↗

PubMed2025

Inference and visualization of complex genotype-phenotype maps with gpmap-tools.

Understanding how biological sequences give rise to observable traits, that is, how genotype maps to phenotype, is a central goal in biology. Yet our knowledge of genotype-phenotype maps in natural systems is limited due to the high dimensionality of sequence space and the context-dependent effects of mutations. The emergence of Multiplex assays of variant effect (MAVEs), along with large collections of natural sequences, offer new opportunities to empirically characterize these maps at an unprecedented scale. However, tools for statistical and exploratory analysis of these high-dimensional data are still needed. To address this gap, we developed gpmap-tools (https://github.com/cmarti/gpmap-tools), a python library that integrates a series of models for inference, phenotypic imputation, and error estimation from MAVE data or collections of natural sequences in the presence of genetic interactions of every possible order. gpmap-tools also provides methods for summarizing patterns of epistasis and visualization of genotype-phenotype maps containing up to millions of genotypes. To demonstrate its utility, we used gpmap-tools to infer genotype-phenotype maps containing 262,144 variants of the Shine-Dalgarno sequence from both genomic 5'UTR sequences and experimental MAVE data. Visualization of the inferred landscapes consistently revealed high-fitness ridges that link core motifs at different distances from the start codon. In summary, gpmap-tools provides a flexible, interpretable framework for studying complex genotype-phenotype maps, opening new avenues for understanding the architecture of genetic interactions and their evolutionary consequences.

Gaussian process↗

PubMed2000

Triangle map: A model of quantum chaos

We study an area preserving parabolic map which emerges from the Poincare map of a billiard particle inside an elongated triangle. We provide numerical evidence that the motion is ergodic and mixing. Moreover, when considered on the cylinder, the motion appears to follow a Gaussian diffusive process.

Journal Article↗

PubMed1992

A unified approach to modeling the backscattered Doppler ultrasound from blood.

A unified approach to modeling the backscattered Doppler ultrasound signal from blood is presented. The approach consists of summing the contributions from elemental acoustic voxels each containing many red blood cells (RBC's). For an insonified region that is large compared to a wavelength, it is shown that the Doppler signal is a Gaussian random process that arises from fluctuation scattering, which implies that the backscattered power is proportional to the variance of local RBC concentrations. As a result, some common misconceptions about the relationship between the backscattering coefficient and hematocrit can be readily resolved. The unified approach was also used to derive a Doppler signal simulation model which shows that, regardless of flow condition, the power in the Doppler frequency spectrum is governed by the exponential distribution. For finite beamwidth and paraxial flow, it is further shown that the digitized Doppler signal can be modeled by a moving average random process whose order is determined by the signal sampling rate as well as the flow velocity profile.

Biophysical Phenomena↗

PubMed1991

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals.

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals are investigated by using digitized RF signals that have been compressed in a commercially made ultrasonic B-scan imaging instrument. Amplitude distributions of compressed RF and video signals were obtained from regions of B-scan images that correspond to approximately the same physical region in a random medium model with known backscatter amplitude characteristics. The amplitude distribution of the signal before compression was obtained by using a table constructed from measurements of the imaging instrument compression characteristics as a function of time gain compensation. While the results indicate the general form of the decompressed data agrees with single parameter model curves that are predicted by a widely employed Gaussian random process model, the signal-to-noise ratios of the decompressed envelope vary up to 20% from the 1.91 value predicted that model. This implies that effects such as nonlinearities, envelope smoothing, and noise which all may be present in varying degrees in practical ultrasonic imaging instrumentation can cause appreciable departures from theoretical data even under highly controlled conditions.

Data Collection↗

PubMed1987

Effect of interbreath fluctuations on characterizing exercise gas exchange kinetics.

Breathing has inherent irregularities that produce breath-to-breath fluctuations ("noise") in pulmonary gas exchange. These impair the precision of characterizing nonsteady-state gas exchange kinetics during exercise. We quantified the effects of this noise on the confidence of estimating kinetic parameters of the underlying physiological responses and hence of model discrimination. Five subjects each performed eight transitions from 0 to 100 W on a cycle ergometer. Ventilation, CO2 output, and O2 uptake were computed breath by breath. The eight responses were interpolated uniformly, time aligned, and averaged for each subject; and the kinetic parameters of a first-order model (i.e., the time constant and time delay) were then estimated using three methods: linear least squares, nonlinear least squares, and maximum likelihood. The breath-by-breath noise approximated an uncorrelated Gaussian stochastic process, with a standard deviation that was largely independent of metabolic rate. An expression has therefore been derived for the number of square-wave repetitions required for a specified parameter confidence using methods b and c; method a being less appropriate for parameter estimation of noisy gas exchange kinetics.

Adult↗

PubMed1993

Optimal radiation beam profiles considering uncertainties in beam patient alignment.

The often large uncertainties that exist in beam patient alignment during radiation therapy may require modification of the incident beams to ensure an optimal delivered dose distribution to the target volume. This problem becomes increasingly severe when the required dose distribution of the incident beams becomes more heterogeneous. A simple analytical formula is derived for the case when the fraction number is high, and the desired relative dose variations are small. This formula adjusts the fluence distribution of the incident beam so that the resultant dose distribution will be as close as possible to the desired one considering the uncertainties in beam patient alignment. When sharp dose gradients are important, for instance at the border of the target volume, the problem is much more difficult. It is shown here that, if the tumor is surrounded by organs at risk, it is generally best to open up the field by about one standard deviation of the positional uncertainty--that is sigma/2 on each side of the target volume. In principle it is simultaneously desirable to increase the prescribed dose by a few per cent compared to the case where the positional uncertainty is negligible, in order to compensate for the rounded shoulders of the delivered dose distribution. When the tissues surrounding the tumor no longer are dose limiting even larger increases in field size may be advantageous. For more critical clinical situations the positional uncertainty may even limit the success of radiotherapy. In such cases one generally wants to create a steeper dose distribution than the underlying random Gaussian displacement process allows. The problem is then best handled by quantifying the treatment outcome under the influence of the stochastic process of patient misalignment. Either the coincidence with the desired dose distribution, or the expectation value of the probability of achieving complication-free tumor control is maximized under the influence of this stochastic process. It is shown that the most advantageous treatment is to apply beams that are either considerably widened or slightly widened and over flattened near the field edges for small and large fraction numbers respectively.

Dose-Response Relationship, Radiation↗

PubMed1992

Testing the Gaussianity of the human EEG during anesthesia.

The Gaussian properties of human EEGs, which were measured over various stages of general anesthesia, were tested. The basis of the method was to describe the EEG signals by autoregressive models and to test the normality of the regression residuals with the Shapiro-Wilk statistic. The results show that in general the human EEG during anesthesia can be considered as a realization of a Gaussian stochastic process.

Anesthesia, General↗

PubMed1995

[Stochastic models of neuronal activity].

Techniques for modeling of a stochastic activity of neurons are briefly reviewed. Our model is proposed, some experimental results with input Gaussian stochastic processes are discussed, and the concept of e-curves is introduced.

Models, Neurological↗

PubMed1995

[A model of stochastic activity of the neuron].

Action Potentials↗