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PubMed2006

Uncertainty estimation by convolution using spatial statistics.

Kriging has proven to be a useful tool in image processing since it behaves, under regular sampling, as a convolution. Convolution kernels obtained with kriging allow noise filtering and include the effects of the random fluctuations of the experimental data and the resolution of the measuring devices. The uncertainty at each location of the image can also be determined using kriging. However, this procedure is slow since, currently, only matrix methods are available. In this work, we compare the way kriging performs the uncertainty estimation with the standard statistical technique for magnitudes without spatial dependence. As a result, we propose a much faster technique, based on the variogram, to determine the uncertainty using a convolutional procedure. We check the validity of this approach by applying it to one-dimensional images obtained in diffractometry and two-dimensional images obtained by shadow moire.

Algorithms↗
PubMed1994

Estimation of evolutionary distances between nucleotide sequences.

A formal mathematical analysis of the substitution process in nucleotide sequence evolution was done in terms of the Markov process. By using matrix algebra theory, the theoretical foundation of Barry and Hartigan's (Stat. Sci. 2:191-210, 1987) and Lanave et al.'s (J. Mol. Evol. 20:86-93, 1984) methods was provided. Extensive computer simulation was used to compare the accuracy and effectiveness of various methods for estimating the evolutionary distance between two nucleotide sequences. It was shown that the multiparameter methods of Lanave et al.'s (J. Mol. Evol. 20:86-93, 1984), Gojobori et al.'s (J. Mol. Evol. 18:414-422, 1982), and Barry and Hartigan's (Stat. Sci. 2:191-210, 1987) are preferable to others for the purpose of phylogenetic analysis when the sequences are long. However, when sequences are short and the evolutionary distance is large, Tajima and Nei's (Mol. Biol. Evol. 1:269-285, 1984) method is superior to others.

Base Sequence↗
PubMedDate not supplied

Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results.

We present a description, biological results and a reliability analysis for the method of diffusion tensor tracking (DTT) of white matter fiber pathways. In DTT, diffusion-tensor MRI (DT-MRI) data are collected and processed to visualize the line trajectories of fiber bundles within white matter (WM) pathways of living humans. A detailed description of the data acquisition is given. Technical aspects and experimental results are illustrated for the geniculo-calcarine tract with broad projections to visual cortex, occipital and parietal U-fibers, and the temporo-calcarine ventral pathway. To better understand sources of error and to optimize the method, accuracy and precision were analyzed by computer simulations. In the simulations, noisy DT-MRI data were computed that would be obtained for a WM pathway having a helical trajectory passing through gray matter. The error vector between the real and ideal track was computed, and random errors accumulated with the square root of track length consistent with a random-walk process. Random error was most dependent on signal-to-noise ratio, followed by number of averages, pathway anisotropy and voxel size, in decreasing order. Systematic error only occurred for a few conditions, and was most dependent on the stepping algorithm, anisotropy of the surrounding tissue, and non-equal voxel dimensions. Both random and systematic errors were typically below the voxel dimension. Other effects such as track rebound and track recovery also depended on experimental conditions. The methods, biological results and error analysis herein may improve the understanding and optimization of DTT for use in various applications in neuroscience and medicine.

Adult↗
PubMed2003

A synfire chain in layered coincidence detectors with random synaptic delays.

In this paper we analyze a synfire chain in a spiking neuron network. We also employ a coincidence-detector model showing the characteristics of temporal information processing more directly than the integrate-and-fire (I&F) model often discussed in the literature. There are two sources of randomness in a feed-forward network, however, only randomness in input spikes has attracted the attention of researchers and the randomness in synaptic delays has largely been ignored. Theoretical analyses of the synfire chain in I&F neurons without randomness in synaptic delays have shown that the dynamics of pulse packets can be viewed as a shift of the membrane potential distribution made by random noise input spikes. We introduce jittered synaptic delays instead of random noise inputs in a network of coincidence detectors and show that the network has almost the same dynamics as that of the I&F neurons. The distribution of the output spikes can be approximately described by an ordinary differential equation useful in understanding the dynamics of the pulse packets.

Algorithms↗
PubMed1998

The statistical distribution of wrist movements during sleep.

The purpose of this work was to describe the basic statistical properties of the process of production of movements measured with a wrist actimeter, along a complete sleep period in normal human subjects. Two distinct types of random magnitudes were considered to analyze the data, the times between successive groups of movements and the number of movements at each fixed time (1 min) measurement epoch. Suitable probabilistic models for the two variates were chosen, fitting theoretical distribution functions to the observed data. It is concluded that interval data fit a one-parameter exponential distribution, while the number of movements fit a two-parameter negative binomial distribution. The estimated values of these parameters, besides being necessary to perform further statistical analysis, are a measure of the intensity and frequency of the movements. Finally the relationship between polysomnography measures and the elicited parameters was studied.

Adult↗
PubMed2003

On episode sensitization in recurrent affective disorders: the role of noise.

Episode sensitization is postulated as a key mechanism underlying the long-term course of recurrent affective disorders. Functionally, episode sensitization represents positive feedback between a disease process and its disease episodes resulting in a transition from externally triggered to autonomous episode generation. Recently, we introduced computational approaches to elucidate the functional properties of sensitization. Specifically, we considered the dynamics of episode sensitization with a simple computational model. The present study extends this work by investigating how naturally occurring, internal or external, random influences ("noise") affect episode sensitization. Our simulations demonstrate that actions of noise differ qualitatively in dependence on both the model's activity state as well as the noise intensity. Thereby induction as well as suppression of sensitization can be observed. Most interestingly, externally triggered sensitization development can be minimized by tuning the noise to intermediate intensities. Our findings contribute to the conceptual understanding of the clinical kindling model for affective disorders and also indicate interesting roles for random fluctuations in kindling and sensitization at the neuronal level.

Electricity↗
PubMed1999

Dose-response relationships in chemical carcinogenesis reflect differences in individual susceptibility. Consequences for cancer risk assessment, extrapolation, and prevention.

The shape of the dose-cancer incidence curve observed in an animal bioassay for carcinogenicity of a chemical is the result of a superposition of various mechanisms contributing to the process of carcinogenesis. For genotoxic carcinogens, for instance, a sublinear (convex; up-bent) shape could be the result of a saturation of DNA repair or of a higher rate of cell turnover associated with high-dose cytotoxicity and regenerative hyperplasia. In human cancer epidemiology, the situation is more complex. The human population is very heterogeneous with respect to both genetic and life-style factors that modulate the process of tumor formation. Therefore, individuals are expected to show widely variable susceptibility to carcinogenic factors, and the dose-response curve is in fact a reflection of the tolerance distribution. Each modulating factor divides the population up into subpopulations of different susceptibility so that nonlinearities that could be present in a homogeneous population are flattened out. A linear extrapolation of a human cancer risk to low dose might therefore be appropriate under certain conditions even if the dose-response curve in animals has a strongly sigmoidal shape. For cancer prevention, the investigation of susceptibility factors is expected to be of great value. The elimination of concurrent risk factors in high-risk subpopulations or individuals might be more effective than a minor general reduction of a tolerable exposure level.

Animals↗
PubMed2005

Topology of biological networks and reliability of information processing.

Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic networks or neurons in the nervous system, are far from being reliable dynamical elements. How can networks of unreliable elements perform reliably? We here address this question in networks of autonomous noisy elements with fluctuating timing and study the conditions for an overall system behavior being reproducible in the presence of such noise. We find a clear distinction between reliable and unreliable dynamical attractors. In the reliable case, synchrony is sustained in the network, whereas in the unreliable scenario, fluctuating timing of single elements can gradually desynchronize the system, leading to nonreproducible behavior. The likelihood of reliable dynamical attractors strongly depends on the underlying topology of a network. Comparing with the observed architectures of gene regulation networks, we find that those 3-node subgraphs that allow for reliable dynamics are also those that are more abundant in nature, suggesting that specific topologies of regulatory networks may provide a selective advantage in evolution through their resistance against noise.

Biological Evolution↗
PubMed1984

A new method for calculating evolutionary substitution rates.

In this paper we present a new method for analysing molecular evolution in homologous genes based on a general stationary Markov process. The elaborate statistical analysis necessary to apply the method effectively has been performed using Monte Carlo techniques. We have applied our method to the silent third position of the codon of the five mitochondrial genes coding for identified proteins of four mammalian species (rat, mouse, cow and man). We found that the method applies satisfactorily to the three former species, while the last appears to be outside the scope of the present approach. The method allows one to calculate the evolutionarily effective silent substitution rate (vs) for mitochondrial genes, which in the species mentioned above is 1.4 X 10(-8) nucleotide substitutions per site per year. We have also determined the divergence time ratios between the couples mouse-cow/rat-mouse and rat-cow/rat-mouse. In both cases this value is approximately 1.4.

Animals↗
PubMed2006

Modeling the effect of inbreeding among founders in linkage analysis.

In this paper, we present a unified mathematical model for linkage analysis that allows for inbreeding among founders in all families. The identical by descent (IBD) configuration of each pedigree is modeled as a Markov process containing two parameters; the inverse inbreeding and kinship coefficient and a rate parameter proportional to the inverse expected length of chromosome segments shared IBD by two different founder haplotypes. We use hidden Markov models and define a forward-backward algorithm for computing the conditional IBD-distribution given marker data, thereby extending the multipoint method of Lander and Green [1987. Construction of multilocus genetic maps in humans, Proc. Natl. Acad. Sci. USA 84, 2363-2367] to situations where founders are inbred. Our methodology is valid for arbitrary pedigree structures. Simulation and theoretical approximations for nonparametric linkage (NPL) analysis based on affected sib pairs reveal that NPL scores are inflated and type 1 errors increased when the inbreeding coefficient or rate parameter is underestimated. When the parents are genotyped, we present a general way of modifying the score function to drastically reduce this effect.

Algorithms↗
PubMed2005

A modeling approach to the impact of HIV mutations on the immune system.

A dynamical system modeling the HIV infection, including a mutation occurrence process, is used, after simplifications, to show the impact of the viral diversity on the immune response and disease dynamics, by introducing an indicator of the immune system behavior, the immunological recognition efficacy (IRE) index. The existence, the expression and the stability of the endemically infected steady state of the IRE index-based model, as function of this index, are mathematically analyzed. The monotony of the steady state with respect to the IRE index is studied and an asymptotic analysis of the dynamical system performed. It is shown that the IRE index-based model provides a bound to the responses of the initial complex dynamical system. The biological interpretation of these mathematical results is the exhaustion of the immune system as a consequence of the continuous generation of viral mutants.

CD4 Lymphocyte Count↗
PubMedDate not supplied

[Sleep EEG as a nonlinear dynamic process: a comparison of global correlation dimension of human EEG and measures of linear interdependence between channels].

The goal of this work was to study (1) whether the estimation of correlation dimension (D2) using spatial embedding distinguishes between sleep stages and (2) whether information gained from the application of global D2 is redundant to measures of linear interdependence between channels. Twenty one-channel EEG segments of 12 healthy male subjects recorded during waking and sleep stages REM, I, II, and III-IV (according to the Rechtshaffen and Kales criteria) were analyzed with global (multichannel) D2, mean square correlation coefficients (MS) and proportion of variance accounted for by the first principal component (PC1). D2 was found to decrease progressively from stage I to stage III-IV with D2 values of waking and REM being close to those of stages I and II. MS and PC1 did not distinguish among sleep stages but yielded significant differences between waking and sleep. The results suggest that global D2 extracts information from human EEG. That sort of evidence cannot be obtained with measures of linear interdependence between channels.

Adolescent↗
PubMed2006

Bisexual branching processes in a genetic context: the extinction problem for Y-linked genes.

In this paper the inheritance of a Y-linked gene with alleles R and r in a population with both females and males is modelled using a two-type bisexual branching process. It is assumed that the reproductive distribution associated with the R allele can differ from the associated with the r allele and that females prefer to mate with a male having the R allele rather than with a male with the r allele. Under these assumptions, we provide some conditions for the extinction and/or survival of both alleles in the population. These conditions depend on the magnitudes of the average number of females and males per mating unit. Moreover, the almost sure extinction of the r allele is independent of the behaviour of the R allele. On the other hand, the survival of the R allele with positive probability may depend strongly on the reproductive behaviour of the other allele. Theoretical results are illustrated by means of simulated examples and some open problems are proposed to the reader as conjectures.

Alleles↗
PubMed2004

Noise reduction and convergence of Bayesian algorithms with blobs based on the Huber function and median root prior.

Iterative image reconstruction algorithms have the potential to produce low noise images. Early stopping of the iteration process is problematic because some features of the image may converge slowly. On the other hand, there may be noise build-up with increased number of iterations. Therefore, we examined the stabilizing effect of using two different prior functions as well as image representation by blobs so that the number of iterations could be increased without noise build-up. Reconstruction was performed of simulated phantoms and of real data acquired by positron emission tomography. Image quality measures were calculated for images reconstructed with or without priors. Both priors stabilized the iteration process. The first prior based on the Huber function reduced the noise without significant loss of contrast recovery of small spots, but the drawback of the method was the difficulty in finding optimal values of two free parameters. The second method based on a median root prior has only one Bayesian parameter which was easy to set, but it should be taken into account that the image resolution while using that prior has to be chosen sufficiently high not to cause the complete removal of small spots. In conclusion, the Huber penalty function gives accurate and low noise images, but it may be difficult to determine the parameters. The median root prior method is not quite as accurate but may be used if image resolution is increased.

Algorithms↗
PubMed1996

Theoretical uncertainty of measurements using quantitative polymerase chain reaction.

Current quantitative polymerase chain reaction (PCR) protocols are only indicative of the quantity of a target sequence relative to a standard, because no means of estimating the amplification rate is yet available. The variability of PCR performed on isolated cells has already been reported by several authors, but it could not be extensively studied, because of lack of a system for doing kinetic data acquisition and of statistical methods suitable for analyzing this type of data. We used the branching process theory to simulate and analyze quantitative kinetic PCR data. We computed the probability distribution of the offspring of a single molecule. We demonstrated that the rate of amplication has a severe influence on the shape of this distribution. For high values of the amplification rate, the distribution has several maxima of probability. A single amplification trajectory is used to estimate the initial copy number of the target sequence as well as its confidence interval, provided that the amplification is done over more than 20 cycles. The consequence of possible molecular fluctuations in the early stage of amplification is that small copy numbers result in relatively larger intervals than large initial copy numbers. The confidence interval amplitude is the theoretical uncertainty of measurements using quantitative PCR. We expect these results to be applicable to the data produced by the next generation of thermocyclers for quantitative applications.

Biometry↗
PubMed2005

Hearing what the eyes see: auditory encoding of visual temporal sequences.

When the senses deliver conflicting information, vision dominates spatial processing, and audition dominates temporal processing. We asked whether this sensory specialization results in cross-modal encoding of unisensory input into the task-appropriate modality. Specifically, we investigated whether visually portrayed temporal structure receives automatic, obligatory encoding in the auditory domain. In three experiments, observers judged whether the changes in two successive visual sequences followed the same or different rhythms. We assessed temporal representations by measuring the extent to which both task-irrelevant auditory information and task-irrelevant visual information interfered with rhythm discrimination. Incongruent auditory information significantly disrupted task performance, particularly when presented during encoding; by contrast, varying the nature of the rhythm-depicting visual changes had minimal impact on performance. Evidently, the perceptual system automatically and obligatorily abstracts temporal structure from its visual form and represents this structure using an auditory code, resulting in the experience of "hearing visual rhythms."

Acoustic Stimulation↗
PubMed2005

Life-history invariants with bounded variables cannot be distinguish from data generated by random processes using standard analyses.

A dimensionless approach to the study of life-history evolution has been applied to a wide variety of variables in the search for life-history invariants. This approach usually employs ordinary least squares (OLS) regressions of log-transformed data. In several well-studied combinations of variables the range of values of one parameter is bounded or limited by the value of the other. In this situation, the null hypothesis normally applied to regression analysis is not appropriate. We generate the null expectations and confidence intervals (CI) for OLS and reduced major axis (RMA) regressions using random variables that are bounded in this way. Comparisons of these CI show that, for log-transformed data, the patterns generated by random data and those predicted by life history invariant theory often could not be distinguished because both predict a slope of 1. We recommend that tests based on the putative invariant ratios and not the correlations between the two variables be used in the exploration of life-history invariants using bounded data. Because empirical data are often not normally distributed randomization test may be more appropriate than standard statistical tests.

Biological Evolution↗
PubMed2004

A primer on the study of transitory dynamics in ecological series using the scale-dependent correlation analysis.

Here we describe a practical, step-by-step primer to scale-dependent correlation (SDC) analysis. The analysis of transitory processes is an important but often neglected topic in ecological studies because only a few statistical techniques appear to detect temporary features accurately enough. We introduce here the SDC analysis, a statistical and graphical method to study transitory processes at any temporal or spatial scale. SDC analysis, thanks to the combination of conventional procedures and simple well-known statistical techniques, becomes an improved time-domain analogue of wavelet analysis. We use several simple synthetic series to describe the method, a more complex example, full of transitory features, to compare SDC and wavelet analysis, and finally we analyze some selected ecological series to illustrate the methodology. The SDC analysis of time series of copepod abundances in the North Sea indicates that ENSO primarily is the main climatic driver of short-term changes in population dynamics. SDC also uncovers some long-term, unexpected features in the population. Similarly, the SDC analysis of Nicholson's blowflies data locates where the proposed models fail and provides new insights about the mechanism that drives the apparent vanishing of the population cycle during the second half of the series.

Animals↗