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PubMed1997

Curvilinearity, covariance, and regularity in perceptual groups.

A curvilinear pattern among a series of visual items (e.g., dots) can be regarded as a kind of probabilistic inference, in which each consecutive angle, regarded independently, is more nearly collinear than would be expected by chance alone. This paper investigates judgments of curvilinearity as a function of the joint distribution of successive inter-dot angles. Subjects were asked to classify 4- and 5-dot configurations as having been generated by a curvilinear generating process, vs independently. Their results are distributed as a gaussian over the inter-dot angles with mean 0 deg (collinear), with a negative correlation between successive angles, but negligible correlation between non-successive angles. This suggests that curvilinearity is evaluated in a 4-dot window moving along the chain of dots, evaluating collinearity and smoothness but ignoring higher-order relationships. Moreover, the probabilistic model provides a remarkably precise numeric prediction of the magnitude of the correlation. Subjects also showed a reliable preference for equal spacing of dots along the virtual curve.

Humans↗

PubMedDate not supplied

Summation of spatiotemporal input patterns in leaky integrate-and-fire neurons: application to neurons in the cochlear nucleus receiving converging auditory nerve fiber input.

The response of leaky integrate-and-fire neurons is analyzed for periodic inputs whose phases vary with their spatial location. The model gives the relationship between the spatial summation distance and the degree of phase locking of the output spikes (i.e., locking to the periodic stochastic inputs, measured by the synchronization index). The synaptic inputs are modeled as an inhomogeneous Poisson process, and the analysis is carried out in the Gaussian approximation. The model has been applied to globular bushy cells of the cochlear nucleus, which receive converging inputs from auditory nerve fibers that originate at neighboring sites in the cochlea. The model elucidates the roles played by spatial summation and coincidence detection, showing how synchronization decreases with an increase in both frequency and spatial spread of inputs. It also shows under what conditions an enhancement of synchronization of the output relative to the input takes place.

Action Potentials↗

PubMed2001

Refined scaling hypothesis for breakdown coefficients in turbulence.

We study the statistics of Novikov's breakdown coefficients, which represent ratios between energy dissipation rates at different length scales in turbulence. The distribution of their logarithms is shown to be very closely reproduced by an analytic function that we obtain from a hierarchical stochastic process for the turbulent cascade. Correlations and deviation from Gaussianity in the model are accounted for by two parameters, one of which can be interpreted as a generalized dimension. Finally, we illustrate the lack of power-law scaling in the moments of the breakdown coefficients and propose an analytical approximation scheme for them.

Journal Article↗

PubMed2001

Chaos and the continuum limit in the gravitational N-body problem: integrable potentials.

This paper summarizes a numerical investigation of the statistical properties of orbits evolved in "frozen," time-independent N-body realizations of smooth, time-independent density distributions corresponding to integrable potentials, allowing for 10(2.5) < or = N < or = 10(5.5). Two principal conclusions were reached: (1) In agreement with recent work by Valluri and Merritt, one finds that, in the limit of a nearly "unsoftened" two-body kernel, i.e., V(r) approximately equals (r(2) + epsilon(2))(-1/2) for epsilon --> 0, the value of the largest Lyapunov exponent chi does not decrease systematically with increasing N, so that, viewed in terms of the sensitivity of individual orbits to small changes in initial conditions, there is no sense in which chaos "turns off" for large N. However, it is clear that, for any finite epsilon, chi will tend to zero for sufficiently large N. (2) Even though chi does not decrease for an unsoftened kernel, there is a clear, quantifiable sense in which, as N increases, chaotic orbits in the frozen-N systems remain "close to" integrable characteristics in the smooth potential for progressively longer times. When viewed in configuration or velocity space, or as probed by collisionless invariants like angular momentum, frozen-N orbits typically diverge from smooth potential characteristics as a power law in time, rather than exponentially, on a time scale approximately equals N(p)t(D), with p approximately 1/2 and t(D) a characteristic dynamical, or crossing, time. For the case of angular momentum, the divergence is well approximated by a t(1/2) dependence, so that, when viewed in terms of collisionless invariants, discreteness effects act as a diffusion process that, presumably, can be modeled by nearly white Gaussian noise in the context of a Langevin or Fokker-Planck description. For position and velocity, the divergence is more rapid, characterized by a nearly linear power-law growth, t(q) with q approximately 1, a result that likely reflects the effects of linear phase mixing. The inference that, pointwise, individual N-body orbits can be reasonably approximated by orbits in a smooth potential only for times < N(1/2)t(D) has potential implications for various resonance phenomena that can act in real self-gravitating systems.

Journal Article↗

PubMed2005

Dynamics of poly(ethylene oxide) in a blend with poly(methyl methacrylate): a quasielastic neutron scattering and molecular dynamics simulations study.

In this paper, we have addressed the question of the dynamic miscibility in a blend characterized by very different glass-transition temperatures, Tg, for the components: poly(ethylene oxide) and poly(methyl methacrylate) (PEO/PMMA). The combination of quasielastic neutron scattering with isotopic labeling and fully atomistic molecular dynamics simulations has allowed us to selectively investigate the dynamics of the two components in the picosecond-10 nanoseconds scale at temperatures close and above the Tg of the blend. The main focus was on the PEO component, i.e., that of the lowest Tg, but first we have characterized the dynamics of the other component in the blend and of the pure PEO homopolymer as reference. In the region investigated, the dynamics of PMMA in the blend is strongly affected by the alpha-methyl rotation; an additional process detected in the experimental window 65 K above the blend-Tg can be identified as the merged alphabeta process of this component that shows strong deviations from Gaussian behavior. On the other hand, pure PEO displays entropy driven dynamics up to very large momentum transfers. Such kind of motion seems to freeze when the PEO chains are in the blend. There, we have directly observed a very heterogeneous and moreover confined dynamics for the PEO component. The presence of the hardly moving PMMA matrix leads to the creation of little pockets of mobility where PEO can move. The characteristic size of such confined islands of mobility might be estimated to be of approximately 1 nm. These findings are corroborated by the simulation study, which has been an essential support and guide in our data analysis procedure.

Journal Article↗

PubMed2005

Quantum multimode model of elastic scattering from Bose-Einstein condensates.

Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.

Journal Article↗

PubMed1994

Hermite expansions of compact support waveforms: applications to myoelectric signals.

Nonstationary signals with finite time support are frequently encountered in electrophysiology and other fields of biomedical research. It is often desirable to have a compact description of their shape and of their time evolution. For this purpose, Fourier analysis is not necessarily the best tool. The Hermite-Rodriguez and Associated Hermite basis functions are applied in this work. Both are based on the product of Hermite polynomials and Gaussian functions. Their general properties relevant to biomedical signal processing are reviewed. Preliminary applications are described concerning the analysis and description of: a) test signals such as a square pulse and a single cycle of a sinewave, b) electrically evoked myoelectric signals, and c) power spectra of either voluntary or evoked signals. It is shown that expansions with only five to ten terms provide an excellent description of the computer simulated and real signals. It is shown that these two families of Hermite functions are well suited for the analysis of nonstationary biological evoked potentials with compact time support. An application to the estimation of scaling factors of electrically evoked myoelectric signals is described. The Hermite functions show advantages with respect to the more traditional spectral analysis, especially in the case of signal truncation due to stimulation with interpulse intervals smaller than the duration of the evoked response. Finally, the Hermite approach is found to be suitable for classification of spectral shapes and compression of spectral information of either voluntary or evoked signals. The approach is very promising for neuromuscular diagnosis and assessment because of its capability for information compression and waveform classification.

Electrophysiology↗

PubMed2004

Recognition by symmetry derivatives and the generalized structure tensor.

We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications: 1) tracking cross markers in long image sequences from vehicle crash tests and 2) alignment of noisy fingerprints.

Dermatoglyphics↗

PubMed2003

Experimental evidence by neutron scattering of a crossover from Gaussian to non-Gaussian behavior in the alpha relaxation of polyisoprene.

We report incoherent quasielastic neutron scattering experiments exploring the alpha-relaxation range in polyisoprene over an unprecedented range in momentum transfer Q. The data corroborate and validate earlier molecular dynamics simulations and reveal the existence of a crossover from Gaussian to non-Gaussian character of the main chain protons self-correlation function in the alpha-relaxation regime. The real challenge of the experiment was to push the neutron techniques to cover a Q range as wide as possible. By combining two neutron spin echo spectrometers and a backscattering instrument, we have been able to study the dynamics in a Q range of 0.1 < or = Q < or = 4.7 A(-1). In the low-Q regime the shape of the relaxation function was found to be related to the dispersion of the relaxation times as predicted by the Gaussian assumption. At short distances or large Q, this relationship is strongly violated indicating a non-Gaussian regime. We have performed a detailed comparison between the experiments and simulations at different temperatures and found, apart from a temperature shift, complete agreement. Combining experiments and simulations led to a consistent interpretation in terms of a distribution of jumps underlying the diffusive motion of protons in the alpha process. This model leads to a time-dependent non-Gaussianity parameter that agrees nearly quantitatively with the simulations and exhibits all features resolved so far from various simulations.

Journal Article↗

PubMed1997

Parallel processing by a homogeneous group of coupled model neurons can enhance, reduce and generate signal correlations.

Correlated activities have been proposed as correlates of flexible association and assembly coding. We addressed the basic question of how signal correlations on parallel pathways are enhanced, reduced and generated by homogeneous groups of coupled neurons, and how this depends on the input activities and their interactions with internal coupling processes. For this we simulated a fully connected group of identical impulse-coded neurons with dynamic input and threshold processes and additive or multiplicative lateral coupling. Input signals were Gaussian white noise (GWN), completely independent or partially correlated on a subgroup of the parallel inputs. We show that in states of high average spike rates input-output correlations were weak while the network could generate correlated activities of stochastic, oscillatory and rhythmic bursting types depending exclusively on lateral coupling strength. In states of low average spike rates input-output correlations were high and the network could effectively enhance or reduce differences in spatial correlation applied to its parallel inputs. The correlation differences were more pronounced with multiplicative lateral coupling than with the additive interactions commonly used. As the different modes of correlation processing emerged already by global changes in the average spike rate and lateral coupling strength, we assume that in real cortical circuits changes in correlational processing may also be induced by unspecific modulations of activation and lateral coupling.

Action Potentials↗

PubMedDate not supplied

Gaussian pulse decomposition: an intuitive model of electrocardiogram waveforms.

This study presents a novel approach to modeling the electrocardiogram (ECG): the Gaussian pulse decomposition. Constituent waves of the ECG are decomposed into and represented by Gaussian pulses using an iterative algorithm: the chip away decomposition (ChAD) algorithm. At each iteration, a nonlinear minimization method is used to fit a portion of the ECG waveform with a single Gaussian pulse, which is then subtracted from the ECG waveform. The process iterates on the resulting residual waveform until the normalized mean square error is below an acceptable level. Three different minimization methods were compared for their applicability to the ChAD algorithm; the Nelder-Mead simplex method was found to be more noise-tolerant than the Newton-Raphson method or the steepest descent method. Using morphologically different ECG waveforms from the MIT-BIH arrhythmia database, it was demonstrated that the ChAD algorithm is capable of modeling not only normal beats, but also abnormal beats, including those exhibiting a depressed ST segment, bundle branch block, and premature ventricular contraction. An analytical expression for the spectral contributions of the constituent waves was also derived to characterize the ECG waveform in the frequency domain. The Gaussian pulse model, providing an intuitive representation of the ECG constituent waves by use of a small set of meaningful parameters, should be useful for various purposes of ECG signal processing, including signal representation and pattern recognition.

Algorithms↗

PubMed2006

Multiscale probability density function analysis: non-Gaussian and scale-invariant fluctuations of healthy human heart rate.

For a detailed characterization of intermittency and non-Gaussianity of human heart rate, we introduce an analysis method to investigate the deformation process of the probability density function (PDF) of detrended increments when going from fine to coarse scales. To characterize the scale dependence of the multiscale PDF, we use two methods: 1) calculation of Kullback-Leibler relative entropy; 2) parameter estimation based on Castaing's equation (B. Castaing et al, 1990). We compare scale-dependence of the increment PDFs between actual heart rate fluctuations and artificially generated Gaussian and non-Gaussian noise, including a widely used autoregressive model and a recently proposed multifractal model based on a random cascade process. Our analysis highlights an essential difference between heart rate fluctuations and those generated by other models. The outstanding feature of human heart rate is the robust scale-invariance of the non-Gaussian PDF, which is preserved not only in a quiescent condition, but also in a dynamic state during waking hours, in which the mean level of heart rate is dramatically changing. Our results strongly suggest the need for revising existing models of heart rate variability to incorporate the scale-invariance in the PDF.

Adult↗

PubMed2005

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors.

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B. C. Goodwin, (Academic, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comput. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein and metabolite concentrations. Further, we present results for a three gene case in coregulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological system.

Algorithms↗

PubMed2005

Structure study and luminescence thermochromism in hexanuclear 6-methyl-2-pyridinethiolato copper(I) crystals.

The structure of hexanuclear 6-methyl-2-pyridinethiolato copper(I) [Cu6(6-mpyt)(6)] crystals has been studied by the X-ray diffraction analysis. These crystals show highly efficient luminescence whose color changes drastically from red to green-blue with lowering temperature from room temperature (RT) to liquid nitrogen temperature (LNT). This is a new example of luminescence thermochromism for hexanuclear copper(I) cluster compounds. Two relaxed luminescence bands appear predominantly: one (CC-band), red luminescence appearing in the lower-energy region around 1.8 eV at higher temperature, is assigned to the transition between intramolecular orbitals (MO) of a Cu cluster center (CC), and the other (CT-band), green-blue luminescence appearing at the higher energy side of 2.6 eV than the CC-band at lower temperature, is assigned to a charge transfer (CT) transition from the CC-MO to a ligand MO. Additionally, the CT band can be deconvoluted to two subbands CT(L) and CT(H). The intensities of the CC- and the CT-bands change complementarily with temperature via a thermal activation process, giving the thermochromism. All of these band shapes can be fitted by a Gaussian function, and their widths are fairly large obeying the hyperbolic cotangent law. These features reflect our system to be a strong electron-lattice coupling one. The relaxation process of the photoexcited states is discussed in terms of a configuration coordinate model.

Journal Article↗

PubMed1994

Shapes of cat auditory nerve fiber tuning curves.

Tuning curves of auditory nerve fibers in normal-hearing cats were fitted by a computational model comprising four processes. One process accounts for sensitivity in tuning curve tails and consists of an approximation to bandpass filtering by extracochlear structures. The second and third processes describe passive and active components of basilar membrane (BM) mechanics, respectively. The former consists of a lowpass filter function, which provides baseline threshold sensitivity and filtering above characteristic frequency (CF), and the latter consists of a Gaussian that accounts for sharp tuning and high sensitivity around CF. A fourth process, modeled as a high-pass filter, was needed in many fits to account for breaks and plateaus in threshold sensitivity at frequencies above CF. The latter three processes operated on cochlear spatial coordinates rather than stimulus frequency. The four-process description closely accounted for shapes of most tuning curves. Tuning curve tails possessed minima at 40-80 dB SPL, and minima increased with fiber CF. High-frequency cutoffs of tail filters tended to increase with CF, but low-frequency cutoffs were generally constant across CF. Functions describing tails varied from ear to ear but behaved in a similar manner for fibers from a single ear. Passive components of BM resonances possessed baselines with sensitivities that decreased with CF and cutoff slopes that increased with CF. The magnitude of the active component increased smoothly with CF over an 80 + dB range, and its spatial extent was essentially constant at 1.5 mm or 6% of cochlear length regardless of gain magnitude, fiber CF, or threshold sensitivity. Tuning curves from fibers with high and medium spontaneous rates (SRs) and similar CFs had nearly identical shapes, with the sole difference being essentially constant differences in sensitivity across the entire excitatory frequency range. Tuning curve shapes from fibers with low SRs were more variable. These could either resemble those obtained from similarly-tuned fibers with higher SRs, or they could exhibit lower tip-to-tail ratios and reduced active component magnitudes. The latter were typically associated with low maximum discharge rates.

Acoustic Stimulation↗

PubMed2005

Point process model of 1/f noise vs a sum of Lorentzians.

We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in a power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields 1/f(beta) spectra in a wide range of frequencies. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of 1/f noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of 1/f(beta)noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.

Journal Article↗

PubMed1998

Analysis-synthesis of the phonocardiogram based on the matching pursuit method.

The matching pursuit method of Mallat and Zhang is applied to the analysis and synthesis of phonocardiograms (PCG's). The method is based on a classical Gabor wavelet or time-frequency atom which is the product of a sinusoid and a Gaussian window function. It decomposes a signal into a series of time-frequency atoms by an iterative process based on selecting the largest inner product of the signal (and the subsequent residues) with atoms from a redundant dictionary. The Gaussian window controls the envelope duration and time position of each atom; and the sinusoid represents the frequency. The method was applied to two sets of PCG's: one with very low-noise level and the other with 10% noise energy. Each data base includes 11 PCG's representing the normal and the pathological conditions of the heart. The normalized root-mean-square error (NRMSE) was computed between the original and the reconstructed signals. The results show that the matching pursuit method is very suitable to the transient and complex properties of the PCG's, as it yielded excellent NRMSE's around 2.2% for the two sets of 11 PCG's tested.

Heart Murmurs↗

PubMed2006

A segmentation-based regularization term for image deconvolution.

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.

Algorithms↗