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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↗

PubMed1993

Predictability of normal heart rhythms and deterministic chaos.

The evidence for deterministic chaos in normal heart rhythms is examined. Electrocardiograms were recorded of 29 subjects falling into four groups-a young healthy group, an older healthy group, and two groups of patients who had recently suffered an acute myocardial infarction. From the measured R-R intervals, a time series of 1000 first differences was constructed for each subject. The correlation integral of Grassberger and Procaccia was calculated for several subjects using these relatively short time series. No evidence was found for the existence of an attractor having a dimension less than about 4. However, a prediction method recently proposed by Sugihara and May and an autoregressive linear predictor both show that there is a measure of short-term predictability in the differenced R-R intervals. Further analysis revealed that the short-term predictability calculated by the Sugihara-May method is not consistent with the null hypothesis of a Gaussian random process. The evidence for a small amount of nonlinear dynamical behavior together with the short-term predictability suggest that there is an element of deterministic chaos in normal heart rhythms, although it is not strong or persistent. Finally, two useful parameters of the predictability curves are identified, namely, the 'first step predictability' and the 'predictability decay rate,' neither of which appears to be significantly correlated with the standard deviation of the R-R intervals.

Journal Article↗

PubMed1997

Nonlinear analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by the class Ic drug cibenzoline.

Methods from nonlinear dynamics were applied to test the hypothesis that the dynamics of sustained atrial fibrillation (AF) is modified by the class Ic drug cibenzoline during pharmacological conversion. The experiments were performed in conscious goats in which sustained AF was induced by continuous maintenance of AF via programmed electrical stimulation. Data were collected from electrophysiological experiments in five goats to terminate sustained AF by continuous infusion of cibenzoline. Sets of five unipolar epicardial electrograms of one minute duration were recorded from the left and right atrial free wall during sustained AF (control), and at three episodes during infusion of cibenzoline, when the mean AF interval had been prolonged to 25%, 50% and 85% with respect to control. Ventricular far-field potentials were removed from atrial electrograms by a coherent averaging procedure. Using the Grassberger-Procaccia method, the dynamics of the local atrial electrograms was investigated by estimating the (coarse-grained) correlation dimension and correlation entropy from the correlation integral. The results were related to a recently proposed classification (types I-III) of AF based on the degree of complexity of atrial activation patterns. The coarse-grained correlation dimension D(cg) and entropy K(cg) indicated that sustained AF corresponded to type II. During drug administration the coarse-grained parameters were not significantly different from control. Scaling regions in the correlation integral were observed after infusion of cibenzoline (3 out of 5 goats) suggesting that the drug introduced low-dimensional features (type I) in the dynamics of AF (correlation dimension D ranging from 2.8 to 4.4 and correlation entropy K from 1.6 to 6.2 nats/s). Sinus rhythm recorded shortly after cardioversion was very regular (D<2 and K<3 nats/s). The hypothesis that the electrograms during AF and sinus rhythm were generated by a static transformation of a linear Gaussian random process was rejected using a test for time reversibility. The nonlinear analysis revealed that cibenzoline does not significantly alter the dynamics of sustained AF during pharmacological conversion other than a slowing down of the atrial activation and a somewhat increasing global organization of the atrial activation pattern. The sudden change in the dynamical behavior at cardioversion suggests a mechanism that is reminiscent of a bifurcation. (c) 1997 American Institute of Physics.

Journal Article↗

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↗

PubMed2005

Topological approach to neural complexity.

Considerable effort in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An important quantity which captures fundamental aspects of brain network organization is the neural complexity C(X) introduced by Tononi et al. [Proc. Natl. Acad. Sci. USA 91, 5033 (1994)]. This work addresses the dependence of this measure on the topological features of a network in the case of a Gaussian stationary process. Both analytical and numerical results show that the degree of complexity has a clear and simple meaning from a topological point of view. Moreover, the analytical result offers a straightforward and faster algorithm to compute the complexity of a graph than the standard one.

Animals↗

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↗

PubMed2002

Series expansion calculation of persistence exponents.

We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times Tn = nDeltaT. The probability that (n+1) consecutive values of X have the same sign decays as Pn approximately exp(-theta(D)Tn). We calculate the discrete persistence exponent theta(D) as a series expansion in the correlator C(DeltaT) up to fourteenth order, and extrapolate to DeltaT = 0 using constrained Padé approximants to obtain the continuum persistence exponent thetas. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.

Journal Article↗

PubMed2003

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order alpha, whose fundamental solutions are Levy alpha-stable distributions that exhibit power law decay, x(-(1+alpha)). Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, x(-alpha), of the front's tail.

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↗

PubMed2002

A latent autoregressive model for longitudinal binary data subject to informative missingness.

Longitudinal clinical trials often collect long sequences of binary data. Our application is a recent clinical trial in opiate addicts that examined the effect of a new treatment on repeated binary urine tests to assess opiate use over an extended follow-up. The dataset had two sources of missingness: dropout and intermittent missing observations. The primary endpoint of the study was comparing the marginal probability of a positive urine test over follow-up across treatment arms. We present a latent autoregressive model for longitudinal binary data subject to informative missingness. In this model, a Gaussian autoregressive process is shared between the binary response and missing-data processes, thereby inducing informative missingness. Our approach extends the work of others who have developed models that link the various processes through a shared random effect but do not allow for autocorrelation. We discuss parameter estimation using Monte Carlo EM and demonstrate through simulations that incorporating within-subject autocorrelation through a latent autoregressive process can be very important when longitudinal binary data is subject to informative missingness. We illustrate our new methodology using the opiate clinical trial data.

Algorithms↗

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↗

PubMed2005

Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the microdisplacement measurement.

To provide a theoretical background for the superiority of the signal-domain phase-only correlation (SDPOC) technique proposed here for microdisplacement measurement, we study the first- and the second-order statistical properties of the complex amplitude of an analytic signal of a white-light speckle pattern, under the assumption of a Gaussian random process, and give a formula for the autocorrelation function of the pseudophase associated with the complex analytic signal. Based on these results, we show mathematically that SDPOC has a performance advantage over conventional intensity-based correlation techniques.

Journal Article↗