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Results for “Gaussian process”

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PubMed2001

Signal-to-noise ratio gain in neuronal systems.

We explore the possibility of a signal-to-noise ratio (SNR) gain both in a single neuron and a neuronal network. In the presence of a weak sinusoidal or pulse signal and Gaussian noise, the output SNR can exceed the input SNR over a wide range of noise intensities. The high output SNR and SNR gain can be acquired coincidentally at optimal noise levels. The results further verify that noise can play a constructive role in sensory processing in neuronal systems.

Animals↗

PubMed2004

Practical limitation for continuous-variable quantum cryptography using coherent States.

In this Letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise.

Journal Article↗

PubMed2004

Geometric invariance in image watermarking.

Surviving geometric attacks in image watermarking is considered to be of great importance. In this paper, the watermark is used in an authentication context. Two solutions are being proposed for such a problem. Both geometric and invariant moments are used in the proposed techniques. An invariant watermark is designed and tested against attacks performed by StirMark using the invariant moments. On the other hand, an image normalization technique is also proposed which creates a normalized environment for watermark embedding and detection. The proposed algorithms have the advantage of being robust, computationally efficient, and no overhead needs to be transmitted to the decoder side. The proposed techniques have proven to be highly robust to all geometric manipulations, filtering, compression and slight cropping which are performed as part of StirMark attacks as well as noise addition, both Gaussian and salt & pepper.

Algorithms↗

PubMed2004

Spherical diffusion for 3D surface smoothing.

A diffusion-based approach to surface smoothing is presented. Surfaces are represented as scalar functions defined on the sphere. The approach is equivalent to Gaussian smoothing on the sphere and is computationally efficient since it does not require iterative smoothing. Furthermore, it does not suffer from the well-known shrinkage problem. Evolution of important shape features (parabolic curves) under diffusion is demonstrated. A nonlinear modification of the diffusion process is introduced in order to improve smoothing behavior of elongated and poorly centered objects.

Cephalometry↗

PubMed2005

Microstructural characterization of autogenous laser welds on 316L stainless steel using EBSD and EDS.

This research is concerned with autogenous welding of 316L stainless steel and the microstructure generated by such a process. Autogenous welding does not require a filler material and in this case relies on an initial shallow melt phase to maintain a conduction limited weld. Essentially, a high power laser beam traverses the substrate, with the beam shaped by conventional optics, which produces a Gaussian irradiance distribution; or with a diffractive optical element, used to produce a uniform irradiance distribution. Initial results have shown that due to the nature of the heating cycle, complex microstructures are developed. These fine, complicated microstructures cannot be satisfactorily resolved and quantified using standard optical microscopy techniques. Electron backscatter diffraction (EBSD) and energy dispersive spectroscopy (EDS) have been carried out on a number of different microstructures prepared using a range of welding parameters. It is demonstrated that the simultaneous determination of the chemistry and crystallography is a very useful tool for rapid identification of the different phases formed on solidification as a consequence of varying welding procedures.

Crystallography↗

PubMed2003

Multiecho processing by an echolocating dolphin.

Bottlenose dolphins (Tursiops truncatus) use short, wideband pulses for echolocation. Individual waveforms have high-range resolution capability but are relatively insensitive to range rate. Signal-to-noise ratio (SNR) is not greatly improved by pulse compression because each waveform has small time-bandwidth product. The dolphin, however, often uses many pulses to interrogate a target, and could use multipulse processing to combine the resulting echoes. Multipulse processing could mitigate the small SNR improvement from pulse compression, and could greatly improve range-rate estimation, moving target indication, range tracking, and acoustic imaging. All these hypothetical capabilities depend upon the animal's ability to combine multiple echoes for detection and/or estimation. An experiment to test multiecho processing in a dolphin measured detection of a stationary target when the number N of available target echoes was increased, using synthetic echoes. The SNR required for detection decreased as the number of available echoes increased, as expected for multiecho processing. A receiver that sums binary-quantized data samples from multiple echoes closely models the N dependence of the SNR required by the dolphin. Such a receiver has distribution-tolerant (nonparametric) properties that make it robust in environments with nonstationary and/or non-Gaussian noise, such as the pulses created by snapping shrimp.

Acoustics↗

PubMed2002

On the problem in model selection of neural network regression in overrealizable scenario.

In considering a statistical model selection of neural networks and radial basis functions under an overrealizable case, the problem of unidentifiability emerges. Because the model selection criterion is an unbiased estimator of the generalization error based on the training error, this article analyzes the expected training error and the expected generalization error of neural networks and radial basis functions in overrealizable cases and clarifies the difference from regular models, for which identifiability holds. As a special case of an overrealizable scenario, we assumed a gaussian noise sequence as training data. In the least-squares estimation under this assumption, we first formulated the problem, in which the calculation of the expected errors of unidentifiable networks is reduced to the calculation of the expectation of the supremum of the chi2 process. Under this formulation, we gave an upper bound of the expected training error and a lower bound of the expected generalization error, where the generalization is measured at a set of training inputs. Furthermore, we gave stochastic bounds on the training error and the generalization error. The obtained upper bound of the expected training error is smaller than in regular models, and the lower bound of the expected generalization error is larger than in regular models. The result tells us that the degree of overfitting in neural networks and radial basis functions is higher than in regular models. Correspondingly, it also tells us that the generalization capability is worse than in the case of regular models. The article may be enough to show a difference between neural networks and regular models in the context of the least-squares estimation in a simple situation. This is a first step in constructing a model selection criterion in an overrealizable case. Further important problems in this direction are also included in this article.

Journal Article↗

PubMed2006

Continuous time Markov models for binary longitudinal data.

Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure.

Biometry↗

PubMed2003

Spatially explicit modelling of transgenic maize pollen dispersal and cross-pollination.

Modelling of pollen dispersal and cross-pollination is of great importance for the ongoing discussion on thresholds for the adventitious presence of genetically modified material in food and feed. Two different modelling approaches for pollen dispersal are used to simulate the cross-pollination rate of pollen emerged from an adjacent transgenic crop field. The models are applied to cross-pollination data from field experiments with transgenic maize (Zea mays). The data were generated by an experimental setup specifically designed to suit the demands of mathematical modelling. First a Gaussian plume model is used for the simulation of pollen transport in and from plant canopies. This is a semiempirical approach combining the atmospheric diffusion equation and Lagrangian methodology. The second model is derived from the localised near field (LNF) theory and based on the physical processes in the canopy. Both modelling approaches prove to be appropriate for the simulation of the cross-pollination rates at distances of about 7.5m and more from the transgene source. The simulation of the cross-pollination rate is less precise at the edge of the source plot especially with the LNF theory. However, the simulation results lie within the range of variability of the observations. Concluding can be pointed out that both models might be adapted to other pollen dispersal experiments of different crops and plot sizes.

Environmental Pollution↗

PubMed2001

Reconstruction of chaotic dynamics by on-line EM algorithm.

In this paper, we discuss the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet), which is a network of local linear regression units. The NGnet is trained by an on-line EM algorithm in order to learn the vector field of the chaotic dynamics. We investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. System noise disturbs the system dynamics itself. Observation noise is added when the state variables are observed. It is shown that the trained NGnet is able to reproduce a chaotic attractor, which approximates the complexity and instability of the original chaotic attractor well, even under various noise conditions. The trained NGnet also shows good prediction performance. When only part of the dynamical variables are observed, the delay embedding method is used. The NGnet is then trained to learn the vector field in the delay coordinate space. Experiments show that the chaotic dynamics embedded in the delay coordinate space is able to be learned under the two types of noise.

Algorithms↗

PubMed2003

Symbolic stochastic dynamical systems viewed as binary N-step Markov chains.

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length L are obtained analytically and numerically. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.

Journal Article↗

PubMed2003

Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution.

We evaluate the use of a smoothed space-frequency distribution (SSFD) to retrieve optical phase maps in digital speckle pattern interferometry (DSPI). The performance of this method is tested by use of computer-simulated DSPI fringes. Phase gradients are found along a pixel path from a single DSPI image, and the phase map is finally determined by integration. This technique does not need the application of a phase unwrapping algorithm or the introduction of carrier fringes in the interferometer. It is shown that a Wigner-Ville distribution with a smoothing Gaussian kernel gives more-accurate results than methods based on the continuous wavelet transform. We also discuss the influence of filtering on smoothing of the DSPI fringes and some additional limitations that emerge when this technique is applied. The performance of the SSFD method for processing experimental data is then illustrated.

Journal Article↗

PubMed1988

New method for the analysis of flow cytometric data.

A numerical method for deriving the fractions of cells in different phases of the cell cycle from a single observed DNA histogram is presented. The observed histogram is regarded as a polluted version (containing allocation errors) of the true histogram. A mathematical model is used to describe the pollution process. A theoretical histogram, representing the true histogram, is constructed so that G1 cells are put into one channel and G2M cells into another; the distribution of S cells in between is approximated with a set of harmonic functions. This theoretical histogram is subsequently disturbed with Gaussian dispersion functions to stimulate the pollution, yielding a predicted histogram. Using a maximum likelihood estimation technique, the model parameters are adjusted iteratively, matching the predicted histogram to the actually observed one. With the final parameter values substituted, the corresponding final theoretical histogram is regarded as a reliable reconstruction of the true histogram. From the latter, the required percentages can be read directly. The advantage of this approach over other mathematical analysis methods is that it allows a wide range of different, continuous distributions for relatively few model parameters (thus featuring flexibility and realism and a diminished risk of encountering computational problems). In addition, estimation errors providing a measure of accuracy can be obtained. To test the method, it was used to analyze various observed histograms from the literature that have been obtained by either simulation or actual flow cytometric measurements. The method appeared to perform well, as compared to the reported results of several other methods of analysis applied to the same data.

Cell Separation↗

PubMed2004

Semiclassical theory of electronically nonadiabatic chemical dynamics: incorporation of the Zhu-Nakamura theory into the frozen Gaussian propagation method.

The title theory is developed by combining the Herman-Kluk semiclassical theory for adiabatic propagation on single potential-energy surface and the semiclassical Zhu-Nakamura theory for nonadiabatic transition. The formulation with use of natural mathematical principles leads to a quite simple expression for the propagator based on classical trajectories and simple formulas are derived for overall adiabatic and nonadiabatic processes. The theory is applied to electronically nonadiabatic photodissociation processes: a one-dimensional problem of H2+ in a cw (continuous wave) laser field and a two-dimensional model problem of H2O in a cw laser field. The theory is found to work well for the propagation duration of several molecular vibrational periods and wide energy range. Although the formulation is made for the case of laser induced nonadiabatic processes, it is straightforwardly applicable to ordinary electronically nonadiabatic chemical dynamics.

Journal Article↗

PubMed1992

An image processing workstation for automatic evaluation of human granulocyte motility.

Polymorphonuclear (PMN) motility is currently determined by a method using chemotactic chambers with micropore filters. PMN locomotive capacity is measured by evaluating the maximum distance travelled by the cells, or by counting the number of cells which have moved through the filter. Although in recent years some attempts to improve the analysis of chemotaxis data by computer-assisted systems have been made no technique has been shown capable of both measurement and correlation of these parameters in real time. In the present paper we describe an automated technique, based on a workstation capable of exploring microporous filters employed in chemotactic chambers and of measuring PMN motility in a reliable, reproducible, rapid manner, independent of the subjectivity of the operator. The measurement is carried out by custom software capable of undertaking computerized image analysis of microscopic fields acquired by a TV camera and of driving the motorized microscopic table. Depth of migration, cell distribution at each plane, correlation index of the random behaviour with the model described by a gaussian distribution and data about the patient or assay under study, are computed, displayed, stored in a data base and printed in real time.

Algorithms↗

PubMed2006

Kernel classifier construction using orthogonal forward selection and boosting with Fisher ratio class separability measure.

A greedy technique is proposed to construct parsimonious kernel classifiers using the orthogonal forward selection method and boosting based on Fisher ratio for class separability measure. Unlike most kernel classification methods, which restrict kernel means to the training input data and use a fixed common variance for all the kernel terms, the proposed technique can tune both the mean vector and diagonal covariance matrix of individual kernel by incrementally maximizing Fisher ratio for class separability measure. An efficient weighted optimization method is developed based on boosting to append kernels one by one in an orthogonal forward selection procedure. Experimental results obtained using this construction technique demonstrate that it offers a viable alternative to the existing state-of-the-art kernel modeling methods for constructing sparse Gaussian radial basis function network classifiers that generalize well.

Algorithms↗

PubMed2004

The footprints of visual attention during search with 100% valid and 100% invalid cues.

Human performance during visual search typically improves when spatial cues indicate the possible target locations. In many instances, the performance improvement is quantitatively predicted by a Bayesian or quasi-Bayesian observer in which visual attention simply selects the information at the cued locations without changing the quality of processing or sensitivity and ignores the information at the uncued locations. Aside from the general good agreement between the effect of the cue on model and human performance, there has been little independent confirmation that humans are effectively selecting the relevant information. In this study, we used the classification image technique to assess the effectiveness of spatial cues in the attentional selection of relevant locations and suppression of irrelevant locations indicated by spatial cues. Observers searched for a bright target among dimmer distractors that might appear (with 50% probability) in one of eight locations in visual white noise. The possible target location was indicated using a 100% valid box cue or seven 100% invalid box cues in which the only potential target locations was uncued. For both conditions, we found statistically significant perceptual templates shaped as differences of Gaussians at the relevant locations with no perceptual templates at the irrelevant locations. We did not find statistical significant differences between the shapes of the inferred perceptual templates for the 100% valid and 100% invalid cues conditions. The results confirm the idea that during search visual attention allows the observer to effectively select relevant information and ignore irrelevant information. The results for the 100% invalid cues condition suggests that the selection process is not drawn automatically to the cue but can be under the observers' voluntary control.

Attention↗

PubMedDate not supplied

The separation of parallel visual systems by disease processes.

AIM: to investigate psychophysics and electrophysiology in disease states with altered retinal function. METHODS: determination of colour and luminance contrast sensitivity functions using computer controlled VDUs: recording of flash and pattern ERGs to short and long flashes of coloured lights under differing conditions of light adaptation: recording of pattern ERG. RESULTS: In melanoma-associated retinopathy (MAR) low spatial frequency temporal flicker loss occurs for achromatic Gaussians, but colour Gaussians are seen normally. Low spatial frequency luminance contrast sensitivity and motion losses are severe while red-green gratings are seen normally. In Cuban Tropical Amblyopia, achromatic luminance contrast sensitivity may be normal, in the presence of considerable losses of colour vision, to spatial frequencies as high as 32 c/degree. There are supernormal cone ERGs. CONCLUSIONS: these 2 conditions represent highly selective loss of 'M' and 'P' pathways respectively. Almost the entire 'bell shaped curve' normally represents M activity. In CTA, there may be a selective loss of the receptive field surrounds of P ganglion cells.

Color Perception↗