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The effects of health histories on stochastic process models of aging and mortality.

A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in "fixed frailty" population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95+) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.

Aging↗

Spatial properties of neurons in the monkey striate cortex.

Contrast sensitivity as a function of spatial frequency was determined for 138 neurons in the foveal region of primate striate cortex. The accuracy of three models in describing these functions was assessed by the method of least squares. Models based on difference-of-Gaussians (DOG) functions where shown to be superior to those based on the Gabor function or the second differential of a Gaussian. In the most general case of the DOG models, each subregion of a simple cell's receptive field was constructed from a single DOG function. All the models are compatible with the classical observation that the receptive fields of simple cells are made up of spatially discrete 'on' and 'off' regions. Although the DOG-based models have more free parameters, they can account better for the variety of shapes of spatial contrast sensitivity functions observed in cortical cells and, unlike other models, they provide a detailed description of the organization of subregions of the receptive field that is consistent with the physiological constraints imposed by earlier stages in the visual pathway. Despite the fact that the DOG-based models have spatially discrete components, the resulting amplitude spectra in the frequency domain describe complex cells just as well as simple cells. The superiority of the DOG-based models as a primary spatial filter is discussed in relation to popular models of visual processing that use the Gabor function or the second differential of a Gaussian.

Action Potentials↗

Determination of chromatographic peak parameters by non-linear curve fitting using statistical moments.

There are many methods (manual, computer), which make possible the detailed analysis of chromatographic peak shape. Curve fitting seems to be one of the successful applications of the evaluation of chromatographic signals. In this case, a mathematical function is fitted to the digitized measuring points. Chromatographic elution curves are generally asymmetric, so it is necessary to find the best mathematical function, which corresponds perfectly to the signal form, and then to determine the parameters of the found equation. In this work a modified mathematical function is presented and used for curve fitting, in which the starting parameters are calculated from the statistical moments (retention time, variance, skewness, excess) of the peak shape. The fitting process gives a more accurate and rapid determination of peak shape characteristics, noise filtering and correction of baseline. The suggested modified Gaussian function, the simulated chromatographic peak shapes, the application of the function to the description of real signals and the parameters obtained by the fitting process will be demonstrated.

Journal Article↗

On the simulation of biological diffusion processes.

Many phenomena of interest in biology can be modeled using diffusion processes satisfying a stochastic differential equation. We consider first the stochastic differential equation dX = mu Xdt + sigma X, dW, where W is a standard Wiener process and representing a population growth process. This is simulated using both a strong Euler scheme involving normal pseudorandom numbers and a weak Euler scheme using Bernoulli pseudorandom numbers. Results are given for the mean of X(1) and its 95% confidence intervals for various numbers of simulations. It is found that there are no significant differences between the results obtained by these two schemes at a particular value of the time step, but the weak scheme takes less computer time than the strong scheme. We also consider the process satisfying dX = (-gamma 1X + gamma 2 (1-X))dt + square root of X(1-X)dW, representing a gene frequency under the influence of random mating and mutation. It is similarly found that the results of simulation by the two schemes are not significantly different. It is concluded that in simulations of many biological diffusion processes it is often advantageous to employ a scheme involving Bernoulli rather than Gaussian random variates not only because it involves fewer machine arithmetic operations but also because problems with large jumps that sometimes occur with extreme values of normal variates are less likely, thus enabling one to employ a larger time step with a concomitant saving in machine time.

Computer Simulation↗

Comparison of parzen density and frequency histogram as estimators of probability density functions.

In neurobiology, and in other fields, the frequency histogram is a traditional tool for determining the probability density function (pdf) of random processes, although other methods have been shown to be more efficient as their estimators. In this study, the frequency histogram is compared with the Parzen density estimator, a method that consists of convolving each measurement with a weighting function of choice (Gaussian, rectangular, etc) and using their sum as an estimate of the pdf of the random process. The difference in their performance in evaluating two types of pdfs that occur commonly in quantal analysis (monomodal and multimodal with equidistant peaks) is demonstrated numerically by using the integrated square error criterion and assuming a knowledge of the "true" pdf. The error of the Parzen density estimates decreases faster as a function of the number of observations than that of the frequency histogram, indicating that they are asymptotically more efficient. A variety of "reasonable" weighting functions can provide similarly efficient Parzen density estimates, but their efficiency greatly depends on their width. The optimal widths determined using the integrated square error criterion, the harmonic analysis (applicable only to multimodal pdfs with equidistant peaks), and the "test graphs" (the graphs of the second derivatives of the Parzen density estimates that do not assume a knowledge of the "true" pdf, but depend on the distinction between the "essential features" of the pdf and the "random fluctuations") were compared and found to be similar.

Fourier Analysis↗

Single-sweep analysis of event-related potentials by wavelet networks--methodological basis and clinical application.

OBJECTIVE: Trial-to-trial variabilities in event-related potentials (ERP's), which are neglected by investigating averaged ERP's, can be important to establish group-specific effects in clinical studies. Single ERP responses have to be analyzed to quantify these variations. In order to overcome the disadvantages of existing single-sweep estimators, we have developed a new procedure based on wavelet networks (WN's) and applied this novel approach in a study concerning attention deficit hyperactivity disorder (ADHD) in children. METHOD: WN's represent signals as a linear combination of wavelet nodes, i.e., components characterized by time-frequency features related to the wavelet transformation. In single-sweep analysis, each wavelet node is restricted to a specific region of the time-frequency plane during the recursive WN training process. This is achieved by means of tapering and bandpass filtering with Gaussian functions which are automatically adapted and closely related to the Morlet basis wavelet. The time course of a single event-related response can be reliably estimated. Furthermore, the WN method automatically provides well-defined parameters for single event-related responses, respectively ERP trial-to-trial variabilities. RESULTS: In a psychophysiological study on ADHD using auditory evoked potentials (AEP's), latency and amplitude parameters extracted from averaged ERP's did not reveal any significant differences between 25 control and 25 ADHD boys. In contrast, interesting group-specific differences could be established by WN single-sweep analysis. CONCLUSION: WN single-sweep analysis can be recommended as a sensitive tool for clinical ERP studies which should be applied in addition to the investigation of averaged responses. INDEX TERMS: Attention deficit hyperactivity disorder (ADHD), event-related potentials, single-sweep estimation, single-sweep parameterization, time-frequency method, wavelet networks.

Adolescent↗

Temporal bone volumetric image deblurring in spiral computed tomography scanning.

RATIONALE AND OBJECTIVES: We developed a method for volumetric image deblurring in spiral (helical) computed tomography (CT) scanning with a three-dimensional (3D) Gaussian point spread function (PSF) to improve the quality of temporal bone spiral CT images for assessing the position of cochlear implants electrodes. METHODS: A patient was scanned after cochlear implantation, and the temporal bone was reconstructed into a volume with 128 voxels per dimension, 0.1 mm per voxel side, and x 10 gray-scale expansion. The 3D PSF in spiral CT imaging was assumed to be Gaussian separable transversely and longitudinally. Standard deviations of the PSF were derived and subjectively adjusted. The image was then deconvolved using Wiener filtering and maximum-likelihood deconvolution methods. Image quality was assessed both visually and quantitatively using cross-sectional area at half of the maximum (CAHM) of the implanted array as the figure of merit. RESULTS: Substantial image deblurring was achieved via deconvolution. Subjectively, anatomic structures were more clearly shown. Deconvolution reduced the CAHM by approximately one third, on average. Three-dimensional deconvolution had better image quality than two-dimensional deconvolution. The maximum-likelihood method produced superior image quality but took longer to process relative to Wiener filtering. CONCLUSION: Volumetric image deblurring is practical with a Gaussian PSF. The maximum-likelihood method is preferred if time permits. Deconvolution facilitates the study of fine details of the temporal bone and cochlear implant.

Adult↗

Current algorithms for computed electron beam dose planning.

The field of electron beam dose planning has been in a state of very rapid development during the last decade. The essentially one-dimensional manual corrections used since the beginning of the sixties, has been replaced by at least two- and sometimes three-dimensional computer algorithms capable of taking all irregularities of the body cross-section and the properties of the various tissues into account. This is achieved by dividing the incoming broad beams in a number of narrow pencil beams, the penetration of which can be described by essentially one-dimensional formalisms. The constituent pencil beams are most often described by Gaussian, experimentally or theoretically derived distributions. The accuracy of different dose planning algorithms is discussed in some detail based on their ability to take the different physical interaction processes of high energy electrons into account. It is shown that those programs that take the deviations from the simple Gaussian model into account give the best agreement with experimental results. With such programs a dosimetric relative accuracy of about 5% is generally achieved except in the most complex inhomogeneity configurations. Finally, the present limitations and possible future developments of electron dose planning are discussed.

Computers↗

Re-Os isotopic evidence for long-lived heterogeneity and equilibration processes in the Earth's upper mantle.

The geochemical composition of the Earth's upper mantle is thought to reflect 4.5 billion years of melt extraction, as well as the recycling of crustal materials. The fractionation of rhenium and osmium during partial melting in the upper mantle makes the Re-Os isotopic system well suited for tracing the extraction of melt and recycling of the resulting mid-ocean-ridge basalt. Here we report osmium isotope compositions of more than 700 osmium-rich platinum-group element alloys derived from the upper mantle. The osmium isotopic data form a wide, essentially gaussian distribution, demonstrating that, with respect to Re-Os isotope systematics, the upper mantle is extremely heterogeneous. As depleted and enriched domains can apparently remain unequilibrated on a timescale of billions of years, effective equilibration seems to require high degrees of partial melting, such as occur under mid-ocean ridges or in back-arc settings, where percolating melts enhance the mobility of both osmium and rhenium. We infer that the gaussian shape of the osmium isotope distribution is the signature of a random mixing process between depleted and enriched domains, resulting from a 'plum pudding' distribution in the upper mantle, rather than from individual melt depletion events.

Journal Article↗

Classical phase-space descriptions of continuous-variable teleportation.

The non-negative Wigner function of all quantum states involved in teleportation of Gaussian states using the standard continuous-variable teleportation protocol means that there is a local realistic phase-space description of the process. This includes the coherent states teleported up to now in experiments. We extend the phase-space description to teleportation of non-Gaussian states using the standard protocol and conclude that teleportation of non-Gaussian pure states with a fidelity of 2/3 is a "gold standard" for this kind of teleportation.

Journal Article↗

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions.

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.

Journal Article↗

Localization of cutaneous lesions in digital images.

Digital imaging could potentially provide a rapid, objective, and quantitative means of detecting changes in important skin conditions, especially the dysplasic nevus syndrome. Image analysis techniques can be applied to digital images to automate the search for changes in moles or other features. Consistent determination of lesion boundaries, perimeter, and area in digital images is a vital first step in this process. In this paper, we show how bilaterally symmetric Laplacian-of-a-Gaussian filters can be used to recover the borders of selected lesions while remaining robust with respect to factors such as the camera point spread function and additive noise. Tests on real and synthetic images demonstrate that lesion borders, area, and perimeter can be obtained with a high degree of reliability. Boundaries are routinely found to within +/- 0.2 pixels, and area and perimeter measurements vary by less than 10% when imaging spot targets and actual cutaneous lesions under a realistic range of experimental conditions.

Dysplastic Nevus Syndrome↗

Local polymer dynamics under strong connectivity constraints: the dendrimer case.

The characteristics of local motion are explored by molecular dynamics simulations in a series of AB(2)-type dendrimer melts. Systems of generations 3-5 were simulated in a wide temperature range, allowing the assessment of effects associated with molecular size, proximity to the detected glasslike transitions, and the strong connectivity constraints imposed by the dendritic topology. Investigation of the mechanisms involved in local motion at short temporal and spatial scales revealed the connection between the non-Gaussian nature of monomer displacements to alpha-relaxation and the caging/decaging process under different degrees of confinement. In the latter mechanism, two characteristic localization lengths were identified: at the low temperature limit spatial localization was realized within approximately 10% of the nearest neighbor distance while at temperatures higher than the glass transition, the existence of an analogous length scale is ascribed to the geometric constraints due to the dense connectivity pattern. As the results from this study are discussed in comparison to the behavior observed in linear polymers and supercooled liquids, new insight is provided on the universal/specific mechanisms involved in local dynamics of different glass-forming systems.

Journal Article↗

Transforming reflectance spectra into Munsell color space by using prime colors.

Independent researchers have proved mathematically that, given a set of color-matching functions, there exists a unique set of three monochromatic spectral lights that optimizes luminous efficiency and color gamut. These lights are called prime colors. We present a method for transforming reflectance spectra into Munsell color space by using hypothetical absorbance curves based on Gaussian approximations of the prime colors and a simplified version of opponent process theory. The derived color appearance system is represented as a 3D color system that is qualitatively similar to a conceptual representation of the Munsell color system. We illustrate the application of the model and compare it with existing models by using reflectance spectra obtained from 1,269 Munsell color samples.

Color↗

Pair dynamics in a glass-forming binary mixture: simulations and theory.

We have carried out molecular dynamics simulations to understand the dynamics of a tagged pair of atoms in a strongly nonideal glass-forming binary Lennard-Jones mixture. Here atom B is smaller than atom A (sigma(BB)=0.88sigma(AA), where sigma(AA) is the molecular diameter of the A particles) and the AB interaction is stronger than that given by Lorentz-Berthelot mixing rule (epsilon(AB)=1.5epsilon(AA), where epsilon(AA) is the interaction energy strength between the A particles). The generalized time-dependent pair distribution function is calculated separately for the three pairs (AA, BB, and AB). The three pairs are found to behave differently. The relative diffusion constants are found to vary in the order D(BB)(R)>D(AB)(R)>D(AA)(R), with D(BB)(R) approximately 2D(AA)(R), showing the importance of the hopping process (B hops much more than A). We introduce a non-Gaussian parameter [alpha(P)(2)(t)] to monitor the relative motion of a pair of atoms and evaluate it for all the three pairs with initial separations chosen to be at the first peak of the corresponding partial radial distribution functions. At intermediate times, significant deviation from the Gaussian behavior of the pair distribution functions is observed with different degrees for the three pairs. A simple mean-field (MF) model, proposed originally by Haan [Phys. Rev. A 20, 2516 (1979)] for one-component liquid, is applied to the case of a binary mixture and compared with the simulation results. While the MF model successfully describes the dynamics of the AA and AB pairs, the agreement for the BB pair is less satisfactory. This is attributed to the large scale anharmonic motions of the B particles in a weak effective potential. Dynamics of the next nearest neighbor pairs is also investigated.

Journal Article↗

Martingale integrals over Poissonian processes and the Ito-type equations with white shot noise.

The construction of the Ito-type stochastic integrals and differential equations for compound Poisson processes is provided. The general martingale and nonanticipating properties of the ordinary (Gaussian) Ito theory are conserved. These properties appear particularly important if the stochastic description has to be proposed according to game theory or the linear relaxation (or the exponential growth) requirements. In contrast to the ordinary Ito theory the (uncorrelated) parametric fluctuation of a definite sign can be still modeled by asymmetric white shot noise, so the general scope of applications is not restricted by the positivity requirements. The possible use of the developed formalism in econophysics is addressed.

Journal Article↗

Automatic sorting for multi-neuronal activity recorded with tetrodes in the presence of overlapping spikes.

Multi-neuronal recording is a powerful electrophysiological technique that has revealed much of what is known about the neuronal interactions in the brain. However, it is difficult to detect precise spike timings, especially synchronized simultaneous firings, among closely neighboring neurons recorded by one common electrode because spike waveforms overlap on the electrode when two or more neurons fire simultaneously. In addition, the non-Gaussian variability (nonstationarity) of spike waveforms, typically seen in the presence of so-called complex spikes, limits the ability to sort multi-neuronal activities into their single-neuron components. Because of these problems, the ordinary spike-sorting techniques often give inaccurate results. Our previous study has shown that independent component analysis (ICA) can solve these problems and separate single-neuron components from multi-neuronal recordings. The ICA has, however, one serious limitation that the number of separated neurons must be less than the number of electrodes. The present study combines the ICA and the efficiency of the ordinary spike-sorting technique (k-means clustering) to solve the spike-overlapping and the nonstationarity problems with no limitation on the number of single neurons to be separated. First, multi-neuronal activities are sorted into an overly large number of clusters by k-means clustering. Second, the sorted clusters are decomposed by ICA. Third, the decomposed clusters are progressively aggregated into a minimal set of putative single neurons based on similarities of basis vectors estimated by ICA. We applied the present procedure to multi-neuronal waveforms recorded with tetrodes composed of four microwires in the prefrontal cortex of awake behaving monkeys. The results demonstrate that there are functional connections among neighboring pyramidal neurons, some of which fire in a precise simultaneous manner and that precisely time-locked monosynaptic connections are working between neighboring pyramidal neurons and interneurons. Detection of these phenomena suggests that the present procedure can sort multi-neuronal activities, which include overlapping spikes and realistic non-Gaussian variability of spike waveforms, into their single-neuron components. We processed several types of synthesized data sets in this procedure and confirmed that the procedure was highly reliable and stable. The present method provides insights into the local circuit bases of excitatory and inhibitory interactions among neighboring neurons.

Action Potentials↗

[K+]o clearance in cortex: a new analytical model.

1. It has been suggested that passive diffusion is the principal mechanism of the clearance of locally elevated extracellular potassium, K+o, in the cerebral cortex. This concept was based on the assumption that elevated K+ could be modeled as a point source. In the present study, the functional role of passive diffusion was reevaluated in the anesthetized cat cortex following local electrical stimulation. 2. The initial spatial distribution of extracellular potassium activity, [K+]o, elevated by monopolar stimulation, could be modeled by a two-dimensional Gaussian function at and below the 500-micron cortical depth. Azimuthal symmetry around the stimulating electrode was assumed and cylindrical spatial coordinates were used. 3. The observed clearance of transiently elevated [K+]o as a function of space and time was much more rapid than that predicted by an analytical model consisting of the homogeneous diffusion equation whose initial condition was the Gaussian spatial distribution of [K+]o at the onset of the clearance process. 4. It is concluded that passive diffusion does not significantly contribute to the rapid clearance of locally elevated extracellular potassium in the cortex. Active uptake of potassium by cortical cells should be more seriously considered as being primarily responsible for the potassium clearance.

Adenosine Triphosphatases↗