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PubMed2005

The spontaneous-rate histogram of the auditory nerve can be explained by only two or three spontaneous rates and long-range dependence.

Estimates of the spontaneous discharge rate (SR) of auditory-nerve (AN) fibers are often based on measurements of the average rate over a long (e.g., 30 s) interval. These measurements are important because SR is apparently correlated with other AN properties, such as threshold to acoustic stimuli, shape of rate-level function, recovery from prior stimulation, and certain anatomical characteristics. Furthermore, histograms of SR estimates from large numbers of fibers suggest that they can be divided into two (i.e., low and high) or three (i.e., low, medium, and high) SR classes. Yet, even "simple" statistical estimates, such as average rate, can behave surprisingly poorly for processes with long-range dependence (LRD), which has been found in the spontaneous activity of AN fibers. In particular, LRD greatly increases the variability of estimates of mean discharge rate. We investigated the implications of this effect of LRD for our understanding of the SRs of AN fibers. The fractional-Gaussian-noise-driven Poisson process (fGnDP) was originally developed to model the LRD action-potential trains of AN fibers. Using rate estimates computed from this model, we were able to reproduce the shape of published histograms of SR using only three fixed SR values. Moreover, by using a Poisson-equivalent integrate-and-fire (IF) model in place of the inhomogeneous Poisson process in the fGnDP model, we were able to reproduce SR histograms using only two fixed SR values. These results suggest that AN fibers may have only two or three possible values for their long-term average spontaneous discharge rates. In other words, all "high-SR" neurons may actually have the same underlying SR. Furthermore, both "low-SR" and "medium-SR" neurons may have a single "true" SR value, or these two classes may have two different "true" SR values. Furthermore, the Poisson-equivalent IF model may prove useful in other applications involving the modeling of trains of action potentials.

Action Potentials↗

PubMed1995

Image processing of computerised visual field data.

BACKGROUND: Computerised perimetry is of fundamental importance in assessing visual function. However, visual fields are subject to patient response variability which limits the detection of true visual loss. METHODS: A method of improving the repeatability of visual field data was demonstrated by applying techniques used in image processing. An illustrative sample of nine normals and nine patients with field loss was used. Two successive Humphrey fields were selected for each subject. Repeatability was defined as the standard deviation of the pointwise differences between sensitivity values of the reference field and repeat field. The field data were then separately subjected to Gaussian and median image processing filters and the repeatability was compared with the unprocessed field results. RESULTS: Improvement in repeatability, by a factor of approximately 2, was demonstrated by both processes. CONCLUSION: These techniques may improve the reliable detection of loss of visual function using computerised perimetry.

Adult↗

PubMed1997

Characteristic Functions and Process Identification by Neural Networks.

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide only incomplete or misleading information on the statistical properties of the data. To handle such situations we propose neural network algorithms, with an hybrid (supervised and unsupervised) learning scheme, which constructs the characteristic function of the probability distribution and the transition functions of the stochastic process. Illustrative examples are presented, which include Cauchy and Lévy-type processes.

Journal Article↗

PubMed2001

Integrated random processes exhibiting long tails, finite moments, and power-law spectra.

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution--which can be obtained from our model in certain limits--which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This allows our process to be viewed as a generalization of the Lévy process that has finite moments.

Journal Article↗

PubMed2006

Major depressive episodes and random mood.

CONTEXT: Mathematical models describing changes in mood in affective disorders may assist in the identification of underlying pathologic and neurobiologic mechanisms and in differentiating between alternative interpretations of psychiatric data. OBJECTIVE: Using time-to-event data from a large epidemiologic survey on recovery from major depression, to model the survival probability, in terms of an underlying process, with parameters which might be recognized and influenced in clinical practice. DESIGN: We present a sequential-phase model for survival analysis, which describes depression as a state with or without an additional incubation phase. Recovery is seen as the transition to a nondepressive state. We show that this sequential-phase model finds a microscopic realization in a dynamic description, the random-mood model, which depicts mood as governed by an Ornstein-Uhlenbeck type of stochastic process, driven by intermittent gaussian noise. RESULTS: For reversible depression (80%), the fractional probability of recovery is remarkably independent of the history of the depression. Analysis with the sequential-phase model suggests single exponential decay in this group, possibly with a short incubation phase. Within the random-mood model, the data for this reversibly depressed cohort are compatible with an intermittent noise pattern of stimuli with average spacing of 4 months and incompatible with nonintermittent noise. CONCLUSIONS: Time-to-event data from psychiatric epidemiologic studies can be conceptualized through modeling as intrasubject processes. The proposed random-mood model reproduces the time-to-event data and explains the incubation phase as an artifact due to the inclusion criterion of 14 days in most current psychiatric diagnostic systems. Depression is found to result more often from pileup of negative stimuli than from single life events. Time sequences, generated using the random-mood model, produce power plots, phase-space trajectories, and pair-correlation sums, similar to recent results for individual patients. This suggests possible clinical relevance along with the model's use as a tool in survival analysis.

Affect↗

PubMed2001

Theoretical versus experimental resolution in optical microscopy.

The aim of this article is to compare experimental resolution under different conditions with theoretical resolution predicted using electromagnetic diffraction theory. Imaging properties of fluorescent beads of three different diameters (0.1 microm, 0.2 microm, and 0.5 microm) as well as imaging properties of four different fluorescence-stained DNA targets (ABL gene, BCR gene, centromere 6, and centromere 17) are studied. It is shown how the dependence of the resolution on object size varies with wavelength (520 nm versus 580 nm), type of microscopy (wide-field, confocal using Nipkow disk, confocal laser scanning) and basic image processing steps (median and gaussian filters). Furthermore, specimen influence on the resolution was studied (the influence of embedding medium, coverglass thickness, and depth below the coverglass). Both lateral and axial resolutions are presented. The results clearly show that real objects are far from being points and that experimental resolution is often much worse than the theoretical one. Although the article concentrates on fluorescence imaging using high NA objectives, similar dependence can also be expected for other optical arrangements.

DNA↗

PubMed2005

Noise correlation length effects on a Morris-Lecar neural network.

The role of spatially correlated stochastic perturbations on a Morris-Lecar neural network subject to an aperiodic subthreshold signal is analyzed in detail. Our results suggest that optimum signal-to-noise ratios can be obtained for two critical noise intensities due to the interplay of the subthreshold Poisson process and the correlated Gaussian forcing. For the second peak, most of the cells are periodically excited, the information transfer is enhanced, and a collective behavior develops measured in terms of the averaged activity of the network. The maximum signal-to-noise ratio increases with the correlation length, although it saturates for global coupling. It was found that there is a range of mean frequencies of the subthreshold signal that increases the signal-to-noise ratio output.

Animals↗

PubMed2002

Spatial and temporal processing of threshold data for detection of progressive glaucomatous visual field loss.

OBJECTIVE: To evaluate the effect of spatial and temporal filtering of threshold visual field data on the ability of pointwise linear regression (PLR) to detect progressive glaucomatous visual field loss. METHODS: Longitudinal visual field data (Full-Threshold Program 30-2 test point pattern) were simulated using a computer model of glaucomatous visual field progression. This approach permitted construction of a "gold standard" because matching visual field data without variability could be generated and analyzed. Four clustered progressive defects were produced, consisting of 2, 3, 9, and 18 locations, respectively, each with progression rates of -1 and -2.5 dB/y. Pointwise linear regression was used to identify progressive test locations (criterion for progression of statistically significant slope of < or =-1 dB/y, P<.05). Each visual field series was analyzed after the following 3 procedures: (1) no filtering (unprocessed data), (2) Gaussian spatial possessing (3 x 3 grid), and (3) temporal processing (2 field moving average). The effect of spatial and temporal processing on PLR discriminatory power for progression detection was quantified by comparison with the gold standard. RESULTS: Spatial processing reduced PLR sensitivity to levels below that achieved for analysis of unprocessed data for small progressive defects (< or =9 locations) or at the low true progression rate (-1 dB/y). Under these conditions, spatial processing caused small PLR specificity improvement. Spatial processing only improved PLR sensitivity above unprocessed levels when progressive defects were large and changing rapidly (progression rate of -2.5 dB/y). Temporal processing gave consistent PLR improvement in sensitivity for all defect sizes and true progression rates. Pointwise linear regression sensitivity gain provided by temporal processing allowed progression to be detected 2 to 3 visual fields earlier than for analysis of raw data. Specificity dropped slightly as a result of temporal processing but remained at 89% or above for all conditions studied. CONCLUSIONS: Gaussian spatial processing reduces PLR discriminatory power with low true progression rates or small progressive defect sizes and, therefore, is of limited use for detection of progressive visual field loss. Temporal processing improves the sensitivity of PLR and reduces the number of tests required to detect progressive loss with minimal loss of specificity. CLINICAL RELEVANCE: Image processing techniques can be applied to threshold visual field data to enhance sensitivity or specificity of PLR for the determination of progressive change. This investigation demonstrates that temporal processing may assist with the detection of significant progressive visual field loss with fewer test results than unprocessed data.

Computer Simulation↗

PubMed2006

Stiffness-weighted magnetic resonance imaging.

An imaging method is introduced in which the signal in MR images is affected by the stiffness distribution in the object being imaged. Intravoxel phase dispersion (IVPD) that occurs during MR elastography (MRE) acquisitions decreases the signal in soft regions more than in stiff regions due to changes in shear wave amplitude and wavelength. The IVPD effect is enhanced by lowpass filtering the MR k-space data with a circular Gaussian lowpass filter. A processing method is introduced to take the time series of MRE magnitude images with IVPD and produce a final stiffness-weighted image (SWI) by calculating the minimum signal at each pixel from a small number of temporal samples. The SWI technique is demonstrated in phantom studies as well as in the case of a preserved postmortem breast tissue specimen with a stiff lesion created by focused ultrasound ablation to mimic a breast cancer. When free of significant sources of depth-dependent wave attenuation, interference, and boundary effects, SWI is a simple, fast, qualitative technique that does not require the use of phase unwrapping or inversion algorithms for localizing stiff regions in an object.

Algorithms↗

PubMed1991

Periaqueductal gray spike trains recorded in frontal or horizontal mesencephalic brain slices from the rat.

Spontaneous spike trains were recorded from the periaqueductal gray matter (PAG) in frontal and horizontal mesencephalic slices in order to compare spontaneous activity of the slice preparation to previous in vivo records. The firing rates resembled those recorded in vivo. They were low notwithstanding the fact that the slicing procedure removed tonic inhibitory input to the PAG. The firing rates increased caudo-rostrally, a fact that had not been reported in vivo, and were lower in frontal sections. Several different spike trains were found, described and classified according to their temporal firing patterns. The spike sequences were usually simple stochastic processes, distributed as a Gaussian function with or without stochastic deletion of spikes.

Animals↗

PubMed1969

Statistical analysis of motor unit firing patterns in a human skeletal muscle.

A statistical analysis of the firing pattern of single motor units in the human brachial biceps muscle is presented. Single motor unit spike trains are recorded and analyzed. The statistical treatment of these spike trains is as stochastic point processes, the theory of which is briefly discussed. Evidence is presented that motor unit spike trains may be modelled by a renewal process with an underlying gaussian probability density. Statistical independence of successive interspike intervals is shown using scatter diagrams; the hypothesis of a gaussian distribution is accepted at the 99th percentile confidence limit, chi-square test, in 90% of the units tested. A functional relationship between the mean and standard deviation is shown and discussed; its implications in obtaining sample size are presented in an appendix.The results of higher order analysis in the form of autocorrelograms and grouped interval histograms are presented. Grouped interval histograms are discussed in the context of motor unit data, and used to confirm the hypothesis that a stable probability density function does not represent a good model of the data at this level of analysis.

Action Potentials↗

PubMed2006

Three-dimensional-IR spectroscopy: beyond the two-point frequency fluctuation correlation function.

Three-dimensional-IR spectroscopy is proposed as a new spectroscopic technique that is sensitive to three-point frequency fluctuation correlation functions. This will be important when the statistics of the underlying stochastic process is non-Gaussian, and hence when the system does not follow the linear response hypothesis. Furthermore, a very general classification of nonlinear spectroscopy in terms of higher order frequency fluctuation correlation functions is introduced, according to which certain moments of a multidimensional spectrum are related to certain frequency fluctuation correlation functions. The classification is rigorous in the so-called inhomogeneous limit, but remains valid approximately also when motional narrowing becomes important. The work also puts a recent paper [J. Bredenbeck et al., Phys. Rev. Lett. 95, 083201 (2005)] onto solid theoretical grounds, where we have shown for the first time that fifth-order spectroscopy--in this case transient two-dimensional spectroscopy--is indeed sensitive to the three-point frequency fluctuation correlation function.

Journal Article↗

PubMed2000

A radioiodine speciation, deposition, and dispersion model with uncertainty propagation for the Oak Ridge dose reconstruction.

Between 1944 and 1956, radioactive 131I was released into the atmosphere from operations at the Oak Ridge National Laboratory in Oak Ridge, TN. The releases occurred from stacks and from building vents and openings in three different chemical forms: elemental, organic, and particulate. During their transport in the atmosphere, different forms of iodine react differently with other atmospheric chemicals and moisture, and are removed from the plume at different rates by the processes of dry and wet deposition. A modified Gaussian plume model was developed to address the processes of radioiodine speciation, deposition, depletion, and dispersion in the atmosphere, and to propagate uncertainties in input parameter values through to the ground-level concentrations of 131I in air. A unique approach was used to develop an implicitly correlated set of hourly meteorological parameters for any day of a month for each month of the year from ten years of available data between 1987 and 1996. The model was validated for both annual average and short-term releases. For the annual average releases, the predictions of ground-level concentrations of 131I from the model were within a factor of 2 of measured field data. For two of the three sets of available weekly data, the measurements fell within the 95% subjective confidence interval of model predictions. Predictions of ground-level air concentrations were made on an annual average basis for the entire period of release and on a short-term, episodic basis for a 1954 accident.

Atmosphere↗

PubMed2004

Radiative intermittent events during Fermi's stochastic acceleration.

We investigate the dynamics of a realization of Fermi's relativistic acceleration mechanism that is a charged test particle oscillating between two reflecting plates that move stochastically. By allowing the charge to radiate energy during each collision, we find that the main features of the system are (1) due to the radiation drag the energy gained by the particle is bounded, and (2) the radiated energy represents a typical realization of an on-off intermittent process, due to numerous continuous encounters with a very small emission, interrupted by short and intense bursts of radiation. This intermittent radiative process exhibits non-Gaussian statistical features.

Journal Article↗

PubMed1995

Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown.

Although optimal decision functions for many simple detection/discrimination tasks can be cast in a form linear in the signal data, more complicated tasks require the addition of higher-order terms. This is typically the case when parameter uncertainty is allowed, in imaging for example, for the detection of a target of known size and shape but unknown position in a noise field. The simple task of detecting signals known exactly except for position, specifically detection of a "boxcar" shaped signal on a uniform data trace, has been studied in order to elucidate the relative importance of the first-, second-, or higher-order terms of the likelihood ratio decision rule. Analytical expressions have been developed to describe signal-to-noise ratios relevant for performance evaluation at low signal contrast levels, and computer simulations have been used to evaluate performance at higher contrast. It was found that for this task the first-order term (which corresponds to measuring the mean value of the data) dominates for low contrast signals but is superseded by higher-order terms (which is jth order correspond to the jth-order correlation of the data match filtered with the jth-order correlation of the signal) as contrast is increased. The quadratic term is found to be inferior to the linear term for small contrast and to the cubic for all values of signal contrast if the background is held constant. When the background level is allowed to vary, the performance of the odd-order terms decreases relative to that of the quadratic (and other even-order ones). Various measures of decision function efficiency are compared, demonstrating the severe limitations of using the simple signal-to-noise ratio (SNR) formalism for processes with non-Gaussian-distributed probability density functions. These results are valuable for guiding approaches to computational observers of signal data by showing the range of validity of suboptimal decision functions that are much easier to compute than the exact likelihood ratio solution.

Computer Simulation↗

PubMed1985

Reduced-order autoregressive modeling for center-frequency estimation.

The center frequency of a narrowband, discrete-time random process, such as a reflected ultrasound signal, is estimated from the parameter values of a reduced, second-order autoregressive (AR) model. This approach is proposed as a fast estimator that performs better than the zero-crossing count estimate for determining the center-frequency location. The parameter values are obtained through a linear prediction analysis on the correlated random process, which in this case is identical to the maximum entropy method for spectral estimation. The frequency of the maximum of the second-order model spectrum is determined from these parameters and is used as the center-frequency estimate. This estimate can be computed very efficiently, requiring only the estimates of the first three terms of the process autocorrelation function. The bias and variance properties of this estimator are determined for a random process having a Gaussian-shaped spectrum and compared to those of the ideal FM frequency discriminator, zero-crossing count estimator and a correlation estimator. It is found that the variance values for the reduced-order AR model center-frequency estimator lie between those for the ideal FM frequency discriminator and the zero-crossing count estimator.

Computers↗

PubMed1999

Aging and recognition memory: changes in regional cerebral blood flow associated with components of reaction time distributions.

We used H(2)15O positron emission tomography (PET) to measure age-related changes in regional cerebral blood flow (rCBF) during a verbal recognition memory task. Twelve young adults (20 to 29 years) and 12 older adults (62 to 79 years) participated. Separate PET scans were conducted during Encoding, Baseline, and Retrieval conditions. Each of the conditions involved viewing a series of 64 words and making a two-choice response manually. The complete reaction time (RT) distributions in each task condition were characterized in terms of an ex-Gaussian model (convolution of exponential and Gaussian functions). Parameter estimates were obtained for the mean of the exponential component (tau), representing a task-specific decision process and the mean of the Gaussian component (mu) representing residual sensory coding and response processes. Independently of age group, both tau and mu were higher in the Encoding and Retrieval conditions than in the Baseline condition, and tau was higher during Retrieval than during Encoding. Age-related slowing in task performance was evident primarily in mu. For young adults, rCBF activation in the right prefrontal cortex, in the Retrieval condition, was correlated positively with mu but not with tau. For older adults, rCBF changes (both increases and decreases) in several cortical regions were correlated with both mu and tau. The data suggest that the attentional demands of this task are relatively greater for older adults and consequently lead to the recruitment of additional neural systems during task performance.

Adult↗

PubMed2006

Anomalous surfactant diffusion in a living polymer system.

Random processes are generally described by Gaussian statistics as formulated by the central limit theorem. However, there exists a large number of exceptions to this rule that can be found in a variety of fields. Diffusion processes are often analyzed by the scaling law approximately t2beta, where the second moment of the diffusion propagator or molecular mean square displacement, , in the case of Gaussian diffusion is proportional to t, i.e., beta=1/2. A deviation from Gaussian behavior may be either superdiffusion (beta>1/2) or subdiffusion (beta<1/2). In this paper we demonstrate that all three diffusion regimes may be observed for the surfactant self-diffusion, on the length scale of 10(-6) m and the time scale of 0.02-0.8 s. in a system of wormlike micelles, depending on small variations in the sample composition. The self-diffusion is followed by pulsed gradient NMR where one not only measures the second moment of the diffusion propagator, but actually measures the Fourier transform of the full diffusion propagator itself. A generalized diffusion equation in terms of fractional time derivatives provides a general description of all the different diffusion regimes, and where 1beta can be interpreted as a dynamic fractal dimension. Experimentally, we find beta=1/4 and 3/4, in the regimes of sub- and superdiffusion, respectively. The physical interpretation of the subdiffusion behavior is that the dominating diffusion mechanism corresponds to a lateral diffusion along the contour of the wormlike micelles. Superdiffusion is obtained near the overlap concentration where the average micellar size is smaller so that the center of mass diffusion of the micelles contributes to the transport of surfactant molecules.

Journal Article↗