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PubMed2007

A dual-process integrator-resonator model of the electrically stimulated human auditory nerve.

A phenomenological dual-process model of the electrically stimulated human auditory nerve is presented and compared to threshold and loudness data from cochlear implant users. The auditory nerve is modeled as two parallel processes derived from linearized equations of conductance-based models. The first process is an integrator, which dominates stimulation for short-phase duration biphasic pulses and high-frequency sinusoidal stimuli. It has a relatively short time constant (0.094 ms) arising from the passive properties of the membrane. The second process is a resonator, which induces nonmonotonic functions of threshold vs frequency with minima around 80 Hz. The ion channel responsible for this trend has a relatively large relaxation time constant of about 1 ms. Membrane noise is modeled as a Gaussian noise, and loudness sensation is assumed to relate to the probability of firing of a neuron during a 20-ms rectangular window. Experimental psychophysical results obtained in seven previously published studies can be interpreted with this model. The model also provides a physiologically based account of the nonmonotonic threshold vs frequency functions observed in biphasic and sinusoidal stimulation, the large threshold decrease obtained with biphasic pulses having a relatively long inter-phase gap and the effects of asymmetric pulses.

Auditory Threshold↗

PubMed2006

Applying an interferometric exposure model to analyze the influences of process parameters on the linewidth.

We utilize a modified interferometric exposure model, enhanced with the Beer-Lambert law, to study how some process parameters influence the structural dimensions within the whole exposure area. An experimental apparatus is built to verify the accuracy of this model. The simulation results indicate that when the incident angle is larger than 15 degrees, the effect of the beam deformation cannot be neglected. One cannot readily obtain periodic structures with the same dimensions during static exposure because of the Gaussian distribution of the light intensity. The theoretical results match the experimental ones quite well. The variation of Dill's parameter A has a greater influence on the transmittance and the linewidth when A is decreasing. If a poor contrast fringe is exposed in the photoresist, it will not only cause a greater nonuniformity of the structural dimensions but also a decreased aspect ratio in the structure after the development process.

Journal Article↗

PubMed1999

PFG-omega1-filtered TOCSY experiments for the determination of long-range heteronuclear and homonuclear coupling constants and estimation of J-coupling "crosstalk" artifacts in 2-D omega1-filtered "E. COSY-style" spectra.

We present novel one- and two-dimensional versions of the omega1-filtered TOCSY experiment. These experiments utilize pulsed-field gradient techniques and INEPT-reverse INEPT magnetization transfer to generate heteronuclear filtering by means of coherence pathway selection. The major advantages of this approach are twofold: first, each experiment requires a reasonable number of transmitter pulses, gradient pulses, and delays to implement. Second, the use of z-axis gradients at the beginning and termination of the pulse sequences prevents the recovery of dephased magnetization prior to FID detection. This technique was incorporated into 1-D and 2-D omega1-filtered JXH- and JHH-TOCSY-style experiments. As demonstrated on 15N-enriched peptide samples, the use of the pulsed-field-gradient coherence selection scheme effectively filters out unwanted magnetization components, thereby improving the overall sensitivity of the experiments. In addition to this suite of pulse sequences, we also present a method for correcting the reduction in J-coupling that results from crosspeak shifting in 2-D omega1-filtered E. COSY-style spectra. This correction is applicable to both Lorentzian and Gaussian 2-D crosspeak lineshapes.

Humans↗

PubMed2003

Real-time Kalman filter applied to biomechanical data for state estimation and numerical differentiation.

This study focused on the application of real-time Kalman filters to biomechanical data and, in particular, the simulation environment used to compare the performance of modified and standard two-state Kalman filters when estimating displacement and velocity from noisy displacement data. The modification proposed in this paper was the numerical tachometer, augmented by a median smoother. The numerical tachometer integrated the derivative estimates from finite differences of noisy sampled data into the Kalman filter structure; the median smoother acted before differentiation, to protect from grossly erroneous measurements. The numerical tachometer allowed better fits to the simulated data than can be achieved without it: the root mean square errors decreased by 10% in the displacement domain and by 54% in the velocity domain, for sampling frequencies and signal contamination levels that were typical in human movement sciences. The sensitivity to errors in the modelling of the signal and noise characteristics was less than in the standard filter implementation. The use of the median smoother improved the robustness of the filtering algorithm against additive white Gaussian measurement noise and allowed the cancellation of isolated noise spikes.

Algorithms↗

PubMed2000

Anisotropy of Surface Roughness on Aluminium Sheet Studied by Atomic Force Microscopy.

Atomic force microscope images of aluminium sheet are used to calculate the mean roughness Ra and the root mean square roughness Rq for different directions (theta) across the samples. The angle determined values of Ra(theta) and Rq(theta) are significantly lower in the rolling direction than in any other direction. The results provide a clear demonstration of the vector nature of surface roughness. Local features in an angle determined Ra(theta) profile are also compared with the positions of peaks and valleys in the matching topographical cross-section of the surface running at right angles to theta. It is further found that the distribution of z heights for an imaged sample is usually not Gaussian in shape unless the z heights are measured about mean lines constructed across the surface parallel with the rolling direction. The results are relevant for controlling lubrication performance in the aluminium rolling process.

Journal Article↗

PubMed1995

Daily validation procedure of chromatographic assay using gaussoexponential modelling.

High performance liquid chromatography is one of the most successful analytical methods used for the quantitative determination of drugs in biological samples. However, this method is marked by a lack of performance reproducibility: chromatographic peaks become wider and even asymmetrical as the column ages. These progressive changes in the chromatographic parameters have to be taken into account when evaluating the validation criteria for the method. These criteria change with the ageing process of the column leading to the need for new estimations to assure the quality of the results. Procedures are proposed for the daily determination of some validation criteria using the exponentially modified Gaussian (EMG) model of the chromatographic peak. This modelling has been studied on simulated chromatographic peaks in order to obtain the relationships between chromatographic measurements and EMG parameters.

Chromatography, High Pressure Liquid↗

PubMed2004

Hydrogen motions in the alpha-relaxation regime of poly(vinyl ethylene): a molecular dynamics simulation and neutron scattering study.

The hydrogen motion in poly(vinyl ethylene) (1,2-polybutadiene) in the alpha-relaxation regime has been studied by combining neutron spin echo (NSE) measurements on a fully protonated sample and fully atomistic molecular dynamics simulations. The almost perfect agreement between experiment and simulation results validates the simulated cell. A crossover from Gaussian to non-Gaussian behavior is observed for the intermediate scattering function obtained from both NSE measurements and simulations. This crossover takes place at unusually low Q values, well below the first maximum of the static structure factor. Such anomalous deviation from Gaussian behavior can be explained by the intrinsic dynamic heterogeneity arising from the differences in the dynamics of the different protons in this system. Side group hydrogens show a markedly higher mobility than main chain protons. Taking advantage of the simulations we have investigated the dynamic features of all different types of hydrogens in the sample. Considering each kind of proton in an isolated way, deviations from Gaussian behavior are also found. These can be rationalized in the framework of a simple picture based on the existence of a distribution of discrete jumps underlying the atomic motions in the alpha process.

Journal Article↗

PubMed2001

Constructing, characterizing, and simulating Gaussian and higher-order point distributions.

The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple method for the simulation of this so-called Gauss-Poisson point process is given and illustrated with an example. A comparison of the distribution of galaxies in the PSCz catalog with the Gauss-Poisson process underlines the importance of higher-order correlation functions for the description for the galaxy distribution. The construction of the Gauss-Poisson point process is extended to the n-point Poisson cluster process, now incorporating correlation functions up to nth order. Simulation methods and constraints on the correlation functions are discussed for an n-point case and detailed for a three-point case. As another approach, well suited for strongly clustered systems, the generalized halo model is discussed. The influence of substructure inside the halos on the two- and three-point correlation functions is calculated in this model.

Journal Article↗

PubMed2005

Gain-scheduled controller for the suppression of convection at high Rayleigh number.

Recent studies in the feedback control of Rayleigh-Bénard convection indicate that one can sustain the no-motion state at a moderate supercritical Rayleigh number (Ra) using only proportional compensation. However, stabilization occurs at a much higher Rayleigh number using linear-quadratic-Gaussian (LQG) control synthesis. The restriction is that the convection model is linear. In this paper, we show that a comparable degree of stabilization is achievable for a fully nonlinear convection state. The process is demonstrated in two stages using a fully nonlinear, 3D Boussinseq model, compensated by a reduced-order LOQ controller and a gain-schedule table. In the first stage a fully-developed convective state is suppressed through the control action at a moderate supercritical Ra. After the residual convection decays to a sufficiently small amplitude, in the second stage, we increase the Ra by a large step and switch the compensator gains using the gain-schedule table. During this change the control action is in place. Our nonlinear simulation results suggest that the nonlinear system can be stabilized to the limit predicted by the linear analysis. The simulation shows that the large Ra jump induces a large transient temperature in the conductive component, which appears to have very small impact on the stabilization.

Journal Article↗

PubMed2006

Numerical method for solving stochastic differential equations with dichotomous noise.

We propose a numerical method for solving stochastic differential equations with dichotomous Markov noise. The numerical scheme is formulated such that (i) the stochastic formula used follows the Stratonovich-Taylor form over the entire range of noise correlation times, including the Gaussian white noise limit; and (ii) the method is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the stochastic process expressed in the Stratonovich-Taylor form. We further propose a simplified Taylor scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. The accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions.

Journal Article↗

PubMed2002

Joint entropy maximization in kernel-based topographic maps.

A new learning algorithm for kernel-based topographic map formation is introduced. The kernel parameters are adjusted individually so as to maximize the joint entropy of the kernel outputs. This is done by maximizing the differential entropies of the individual kernel outputs, given that the map's output redundancy, due to the kernel overlap, needs to be minimized. The latter is achieved by minimizing the mutual information between the kernel outputs. As a kernel, the (radial) incomplete gamma distribution is taken since, for a gaussian input density, the differential entropy of the kernel output will be maximal. Since the theoretically optimal joint entropy performance can be derived for the case of nonoverlapping gaussian mixture densities, a new clustering algorithm is suggested that uses this optimum as its "null" distribution. Finally, it is shown that the learning algorithm is similar to one that performs stochastic gradient descent on the Kullback-Leibler divergence for a heteroskedastic gaussian mixture density model.

Algorithms↗

PubMed2006

Soft mixer assignment in a hierarchical generative model of natural scene statistics.

Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

Animals↗

PubMed2005

Introduction to Bayesian methods II: fundamental concepts.

The use of Bayesian design and analysis is burgeoning. In this introduction to Bayesian methods, we provide basic examples of Bayesian thinking and formalism on which more complicated and comprehensive approaches are built. These include adjusting estimates using related information, the use of Bayes theorem in diagnostic testing, the relationship of the prior and posterior distributions for situations where both the data and prior distribution are Gaussian, and the key steps in a Bayesian analysis. If Bayesian methods are carefully developed and applied, they have excellent objective (i.e., frequentist) properties, providing marvelous tools to help improve the FDA regulatory process.

Bayes Theorem↗

PubMed1997

[Employing deconvolution method for correcting scatter in radiography].

It is well known that the scattered-radiation (SR) results in degradation of the images contrast in digital X-ray radiograph. The main reason affecting radiographic image quality is the SR arising from interaction of the photons with object being radiographed and veiling glare from detector system in the II-TV chai imaging system. With the aim of improving the image quality, we employed the Gaussian function to approximate the scattered point spread function (PSF) and determined the fraction of SR, rho and the parameter, sigma experimentally on an individual system; then we built an inverse filter to process the digital chest X-ray images, which were acquired with the same system and transformed in 2-D Fourier tansform operation. The images processed were corrected by using a variable weihting factor and the resulting images are shown in this paper. The method provides a useful way for solving the problem of correction of the SR in digital X-ray images.

Algorithms↗

PubMed2003

Blind deblurring of spiral CT images.

To discriminate fine anatomical features in the inner ear, it has been desirable that spiral computed tomography (CT) may perform beyond their current resolution limits with the aid of digital image processing techniques. In this paper, we develop a blind deblurring approach to enhance image resolution retrospectively without complete knowledge of the underlying point spread function (PSF). An oblique CT image can be approximated as the convolution of an isotropic Gaussian PSF and the actual cross section. Practically, the parameter of the PSF is often unavailable. Hence, estimation of the parameter for the underlying PSF is crucially important for blind image deblurring. Based on the iterative deblurring theory, we formulate an edge-to-noise ratio (ENR) to characterize the image quality change due to deblurring. Our blind deblurring algorithm estimates the parameter of the PSF by maximizing the ENR, and deblurs images. In the phantom studies, the blind deblurring algorithm reduces image blurring by about 24%, according to our blurring residual measure. Also, the blind deblurring algorithm works well in patient studies. After fully automatic blind deblurring, the conspicuity of the submillimeter features of the cochlea is substantially improved.

Algorithms↗

PubMed2004

A method for modeling noise in medical images.

We have developed a method to study the statistical properties of the noise found in various medical images. The method is specifically designed for types of noise with uncorrelated fluctuations. Such signal fluctuations generally originate in the physical processes of imaging rather than in the tissue textures. Various types of noise (e.g., photon, electronics, and quantization) often contribute to degrade medical images; the overall noise is generally assumed to be additive with a zero-mean, constant-variance Gaussian distribution. However, statistical analysis suggests that the noise variance could be better modeled by a nonlinear function of the image intensity depending on external parameters related to the image acquisition protocol. We present a method to extract the relationship between an image intensity and the noise variance and to evaluate the corresponding parameters. The method was applied successfully to magnetic resonance images with different acquisition sequences and to several types of X-ray images.

Algorithms↗

PubMed2005

Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals part II: peak model and deconvolution algorithms.

Several interlinked algorithms for peak deconvolution by non-linear regression are presented. These procedures, together with the peak detection methods outlined in Part I, have allowed the implementation of an automatic method able to process multi-overlapped signals, requiring little user interaction. A criterion based on the evaluation of the multivariate selectivity of the chromatographic signal is used to auto-select the most efficient deconvolution procedure for each chromatographic situation. In this way, non-optimal local solutions are avoided in cases of high overlap, and short computation times are obtained in situations of high resolution. A new algorithm, fitting both the original signal and the second derivatives is proved to avoid local optima in intermediate coelution situations. This allows achieving the global optimum without the need of background knowledge by the user. A previously reported peak model, a Gaussian with a polynomial standard deviation whose complexity can be modulated to enhance the fitting quality, was applied. However, the original formulation was modified to account baseline outside the peak region. Also, the optimal model complexity was auto-selected via error propagation theory. The method is able to process simultaneously several related chromatograms. The software was tested with both simulated and experimental chromatograms obtained with monolithic silica columns.

Algorithms↗

PubMed2004

Prediction of peak shape as a function of retention in reversed-phase liquid chromatography.

Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), peak height (H0), standard deviation at the peak maximum (sigma0), and left (A) and right (B) halfwidths, is proposed. The model is a simplification of a previous equation proposed in our laboratory. Linear and parabolic relationships were found between the peak shape parameters (sigma0), A and B) and tR, with a mean relative error of 1-5% in most cases. This error was partially due to variations in peak position and shape among injections, which in some cases were above 2%. Correlations between (sigma0, A and B) and the retention time, which is easily modelled as a function of mobile phase composition, allowed a simple and reliable prediction of chromatographic peaks. A parameter that depends on the slopes of the linear relationships for A and B versus tR is also proposed to evaluate column efficiency. The modified-Gaussian model was used to describe the peaks of six diuretics of diverse acid-base behaviour and polarity, which were eluted with 15 mobile phases where the composition was varied between 30 and 50% (v/v) acetonitrile and the pH between 3 and 7.

Chromatography, Liquid↗