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PubMed1996

Variability of extracellular spike waveforms of cortical neurons.

1. Here we study the variability in extracellular records of action potentials. Our work is motivated, in part, by the need to construct effective algorithms to classify single-unit waveforms from multiunit recordings. 2. We used microwire electrode pairs (stereotrodes) to record from primary somatosensory cortex of awake, behaving rat. Our data consist of continuous records of extracellular activity and segmented records of extracellular spikes. Spectral and principal component techniques are used to analyze mean single-unit wave-forms, the variability between different instances of a single-unit waveform, and the underlying background activity. 3. The spectrum of the variability between different instances of a single-unit waveforms is not white, and falls off above 1 kHz with a frequency dependence of roughly f-2. This spectrum is different from that of the mean spike waveforms, which falls off roughly as f-4, but is essentially identical with the spectrum of background activity. The spatial coherence of the variability on the 10-micron scale also falls off at high frequencies. 4. The variability between different instances of a single-unit waveform is dominated by a relatively small number of principal components. As a consequence, there is a large anisotropy in the cluster of the spike waveforms. 5. The background noise cannot be represented as a stationary Gaussian random process. In particular, we observed that the spectrum changes significantly between successive 20-ms intervals. Furthermore, the total power in the background activity exhibits larger fluctuations than is consistent with a stationary Gaussian random process. 6. Roughly half of the single-unit spike waveforms exhibit systematic changes as a function of the interspike interval. Although this results in a non-Gaussian distribution in the space of waveforms, the distribution can be modeled by a scalar function of the interspike interval. 7. We use a set of 44 mean single-unit waveforms to define the space of differences between spike waveforms. This characterization, together with that of the background activity, is used to construct a filter that optimizes the detection of differences between single-unit waveforms. Further, an information theoretic measure is defined that characterizes the detectability.

Action Potentials↗
PubMed2002

Persistence of a continuous stochastic process with discrete-time sampling: non-Markov processes.

We consider the problem of "discrete-time persistence," which deals with the zero crossings of a continuous stochastic process X(T) measured at discrete times T=nDeltaT. For a Gaussian stationary process the persistence (no crossing) probability decays as exp(-theta(D)T)=[rho(a)](n) for large n, where a=exp(-DeltaT/2) and the discrete persistence exponent theta(D) is given by theta(D)=(ln rho)/(2 ln a). Using the "independent interval approximation," we show how theta(D) varies with DeltaT for small DeltaT and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015101(R) (2001)] to determine rho(a) for a two-dimensional random walk and the one-dimensional random-acceleration problem. We also consider "alternating persistence," which corresponds to a<0, and calculate rho(a) for this case.

Journal Article↗
PubMed2001

Persistence of a continuous stochastic process with discrete-time sampling.

We introduce the concept of "discrete-time persistence," which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T=n Delta T. For a Gaussian Markov process with relaxation rate mu, we show that the persistence (no crossing) probability decays as [rho(a)](n) for large n, where a = exp(-mu Delta T), and we compute rho(a) to high precision. We also define the concept of "alternating persistence," which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.

Journal Article↗
PubMed2001

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models.

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the "error-correction form") is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Journal Article↗
PubMed1999

Manifestations of slow site exchange processes in solution NMR: a continuous Gaussian exchange model.

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.

Adenine↗
PubMed1989

Applications of the expectation-maximization algorithm to quantal analysis of postsynaptic potentials.

The expectation-maximization (EM) algorithm is a robust method for maximum likelihood estimation of the parameters of an incompletely sampled distribution. It has been used to resolve the trial-to-trial amplitude fluctuations of postsynaptic potentials, when these are recorded in the presence of noise. Its use has however been limited by the need for different recursion equations for each set of conditions defined by the signal and noise processes. These equations are derived for the following conditions which arise in studies of synaptic transmission: non-gaussian noise process; quantal fluctuation; quantal variability. In addition, a constraint can be incorporated to accommodate simple and compound binomial models of transmitter release. Some advantages of these methods are illustrated by Monte Carlo simulations.

Algorithms↗
PubMed2001

Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability.

We consider detection of a nodule signal profile in noisy images meant to roughly simulate the statistical properties of tomographic image reconstructions in nuclear medicine. The images have two sources of variability arising from quantum noise from the imaging process and anatomical variability in the ensemble of objects being imaged. Both of these sources of variability are simulated by a stationary Gaussian random process. Sample images from this process are generated by filtering white-noise images. Human-observer performance in several signal-known-exactly detection tasks is evaluated through psychophysical studies by using the two-alternative forced-choice method. The tasks considered investigate parameters of the images that influence both the signal profile and pixel-to-pixel correlations in the images. The effect of low-pass filtering is investigated as an approximation to regularization implemented by image-reconstruction algorithms. The relative magnitudes of the quantum and the anatomical variability are investigated as an approximation to the effects of exposure time. Finally, we study the effect of the anatomical correlations in the form of an anatomical slope as an approximation to the effects of different tissue types. Human-observer performance is compared with the performance of a number of model observers computed directly from the ensemble statistics of the images used in the experiments for the purpose of finding predictive models. The model observers investigated include a number of nonprewhitening observers, the Hotelling observer (which is equivalent to the ideal observer for these studies), and six implementations of channelized-Hotelling observers. The human observers demonstrate large effects across the experimental parameters investigated. In the regularization study, performance exhibits a mild peak at intermediate levels of regularization before degrading at higher levels. The exposure-time study shows that human observers are able to detect ever more subtle lesions at increased exposure times. The anatomical slope study shows that human-observer performance degrades as anatomical variability extends into higher spatial frequencies. Of the observers tested, the channelized-Hotelling observers best capture the features of the human data.

Artifacts↗
PubMed2001

Simulation of jet-noise excitation in an acoustic progressive wave tube facility.

Acoustic excitation produced by jet-engine effluxes was simulated in a progressive wave tube (APWT) facility with a computer-based control system. The APWT siren is driven by a signal generated numerically in a PC and then converted into analog form. Characteristics of the acoustic pressure measured by a microphone are analyzed in digital form and compared with those prescribed for simulation. Divergence is compensated by immediate modification of the driving signal and this action is repeated in the form of iterative process until the test specification is attained. Typical power spectral density (PSD) shapes with maxima at low and high frequencies were simulated. A "tailoring" approach has been also achieved when a test specification was determined directly from field measurements for the particular aircraft under consideration. Since acoustic pressure signals of high level differ from the Gaussian random process model, particularly in terms of asymmetric probability density function, a method has been developed to make the driving signal also non-Gaussian by simulating skewness and kurtosis parameters of the APWT acoustic excitation simultaneously with PSD control. Experimental results with Gaussian and non-Gaussian characteristics obtained for various PSD specifications including sharp and narrow peaks are presented in the paper.

Journal Article↗
PubMed1993

Characterization of the dynamic stress response of manual and powered wheelchair frames.

Two wheelchairs, one manual, one electrically powered, were instrumented with strain gages and operated over various laboratory terrains. Both wheelchairs were folding models with cross tubes pinned together at the center. The wheelchairs were operated on a constant speed treadmill with no bump, and with 0.953 cm (0.375 in) and 1.6 cm (0.625 in) dowels simulating bumps. The wheelchairs were also rolled off a 10.8 cm (4.25 in) platform to simulate a curb drop. The von Mises stresses were computed from the recorded strains, and statistical hypothesis tests were performed to determine whether the stresses were consistent with a stationary, narrow-band Gaussian random process. Such a stress history has been used in random fatigue analyses. Summary data for two strain gage locations on each wheelchair, for the four different test terrains, suggest that the von Mises stress can be considered stationary, but neither narrow-banded, nor Gaussian distributed.

Humans↗
PubMed2003

Anomalous transport of particle tracers in multidimensional cellular flows.

Advection of tracers is studied numerically in time-dependent, two-dimensional cellular flows and a time-independent, three-dimensional cellular flow field. Tracers in these flows follow trajectories that are either periodic or chaotic and mimic correlated Lévy flights. The probability density function of displacements for particles in the ordered regions of the flow follows a classical Gaussian dispersion process. The particle trajectories in the chaotic regions of the flow exhibit anomalous diffusion and the probability density function of displacements is well modeled by a time-fractional diffusion equation of order alpha. The overall process of particle dispersion is found to be controlled mainly by the chaotic regions within the flow field. From the perspective of Lagrangian dynamics our results indicate that the advection of particles in flow fields prone to exhibit chaotic advection is a combination of both classical, i.e., Gaussian, behavior and anomalous, i.e., non-Gaussian, diffusion.

Journal Article↗
PubMed1997

Non-Gaussian statistical property of the ultrasonic Doppler signal downstream of a severe stenosis.

The Doppler signal is generally considered as a Gaussian random process. However, to date very little experimental validation of this model has been available. Recently, the K model was proposed to describe the statistical properties of ultrasonic radio frequency signals and their envelopes. The coefficient of kurtosis, which has been shown to be related to the parameters of the K model, was used in the literature as an index to assess the deviations from the Gaussian statistical property of ultrasonic signals obtained from simulations, phantoms and tissues. In the present study, an in vitro flow loop model was used to evaluate the effect of a severe stenosis on the coefficient of kurtosis. Our results showed non-Gaussian statistical properties of the Doppler signal in the jet of the stenosis.

Constriction, Pathologic↗
PubMedDate not supplied

The effect of digital unsharp-mask filtering on the signal-to-noise ratio in computed radiography.

The effect of image processing in computed radiography (CR) has been analyzed in many ROC studies. The results have not shown great diagnostic improvements, except in some special occasions. The theoretical effect of image enhancement on the signal-to-noise ratio in CR images has so far not been assessed. Concerning the previous results, the changes induced in the signal-to-noise ratio by digital image processing are certainly of interest. We calculated the signal-to-noise ratio in various conditions according to the principles of the Rose model, using the computerized image data of storage phosphor radiography. Seventy-seven computed radiographs processed by Gaussian unsharp-mask filtering using different kernel widths were analyzed. The signal-to-noise ratio was reduced in all images by more than 40% when the smallest kernels were used, and increased slowly towards the original value with greater kernel sizes. In no conditions did the ratio exceed the original one. The results show that although edges and signal contrast can be enhanced by unsharp-mask filtering, this happens at the cost of increased noise. This might at least in part explain why image processing does not significantly improve the diagnostic information content of a computed radiograph.

Filtration↗
PubMed2002

Time-dependent structure in the discharge rate of human motor units.

OBJECTIVES: The aim of this study was to examine the influence of visual and motor processes on the deterministic and stochastic structure of force output and motor unit discharge variability. METHODS: Young adult subjects produced continuous, isometric force at 3, 6, 12, and 24% of their maximal voluntary contraction at low and high visual gain levels through abduction of the index finger. Force and fine-wire intramuscular electromyography were recorded. RESULTS: There was a linear increase in discharge irregularity with increases in the mean motor unit discharge rate (8-30 Hz). Recurrence analysis showed that the percentage of deterministic structure in discharge variability remained high, but decreased linearly with increased motor unit discharge rate. Surrogate analyses confirmed that the motor unit discharge variability was inconsistent with an uncorrelated and linearly correlated Gaussian noise process. Spectral analysis revealed that both the force output and the mean time-varying motor unit discharge time series had a dominant frequency of 0-2 Hz. Visual feedback gain did not affect the individual motor unit discharge patterns. CONCLUSIONS: The motor unit discharge rate has deterministic time-dependent structure. The motor unit discharge rate is modulated at multiple time scales likely by pre- and post-synaptic induced fluctuations from spinal level pathways impinging on the motor neuron.

Action Potentials↗
PubMed2002

High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity.

Magnetic resonance (MR) diffusion tensor imaging (DTI) can resolve the white matter fiber orientation within a voxel provided that the fibers are strongly aligned. However, a given voxel may contain a distribution of fiber orientations due to, for example, intravoxel fiber crossing. The present study sought to test whether a geodesic, high b-value diffusion gradient sampling scheme could resolve multiple fiber orientations within a single voxel. In regions of fiber crossing the diffusion signal exhibited multiple local maxima/minima as a function of diffusion gradient orientation, indicating the presence of multiple intravoxel fiber orientations. The multimodality of the observed diffusion signal precluded the standard tensor reconstruction, so instead the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange, and the underlying mixture of tensors was solved for using a gradient descent scheme. The multitensor reconstruction resolved multiple intravoxel fiber populations corresponding to known fiber anatomy. Ma

Anisotropy↗
PubMed1998

Spin Echo Attenuation of Restricted Diffusion as a Discord of Spin Phase Structure

By using the particle probability density we analyze the spin echo attenuation of particles, diffusing in a bounded region. It provides a means to expand a nonuniform spin phase distribution into a series of waves that characterize the geometry and boundary conditions of confinement. Random motion disrupts the initial phase structure created by applied gradients and consequently discords its structure waves. By assuming the spin phase fluctuation and/or the randomness of spin phase distribution in the subensemble as a Gaussian stochastic process, we derive a new analytical expression for the echo attenuation related to the particle velocity correlation. For a diffusion in porous structure we get the expression featuring the same "diffusive diffraction" patterns as those being found and explained by P. T. Callaghan and A. Coy ("Principles of Nuclear Magnetic Resonance Microscopy," Oxford Univ. Press, Oxford (1991); J. Chem. Phys. 101, 4599-4609 (1994)) with the use of propagator theory. With the new approach we cast a new light on the phenomena and derive analitically how the diffusive diffractions appear when the sequence of finite or even modulated gradients are applied. The method takes into account the non-Markovian character of restricted diffusion, and therefore the echo dependence on the diffusion lengths and on the strength of applied gradient differs from the results of authors assuming the Markovian diffusion either by dealing with the diffusion propagators or by the computer simulation of Fick's diffusion. Copyright 1998 Academic Press.

Journal Article↗