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Simulation of the primate motor cortex and free arm movements in three-dimensional space: a robot arm system controlled by an artificial neural network.

It has been recently discovered that neuronal activity in the primate motor cortex varies in an orderly fashion with the direction of movement of behaving monkeys in three-dimensional (3-D) space. Furthermore, cell activity is highest in a certain direction, the cell's preferred direction, and decreases progressively in other directions. For a particular movement direction, each cell makes a contribution in the direction of its preferred direction to yield a neuronal population vector that points in the direction of movement well before the movement begins. Simulation of motor cortical activity is useful with a randomly selected Poisson distribution. Poisson spike trains are used as input to an artificial neural network (ANN) that produces motor actions in the form of a Cartesian coordinate to a PUMA robotic arm system. The ANN consists of a three-layered feed-forward system that uses a specific cosine algorithm as synaptic weights between the interconnected units described in the angle between the preferred direction vector of the neuron and the movement vector. The robot responds to commands, generating actual trajectories in close agreement with desired trajectories. It is shown that the time-varying motor output is controlled by the impulse activity with a good estimate of the direction of movement with 100-150 cells.

Animals↗

Statistics of the LS-detector in the case of low counting efficiency.

In the case of high-quenched 3H and 63Ni sources a distinct incompatibility of theoretical and experimental detection efficiency in the triple liquid scintillation (LS) detector was observed (Appl. Radiat. Isot. 52 (2000) 643). The authors concluded, that the Poisson distribution does not properly describe the detection process, when less than one photoelectron is expected in one of the photomultipliers. Application of other distributions of photoelectrons, e.g. binomial, does not solve the observable problem of incompatibility. Measurements of a set of 55Fe sources have been performed with phototubes defocusing and grey filters for decreasing the counting efficiency of the TDCR detector. Differences between counting results of the 55Fe source and the light emitting diode (LED), simulating the scintillation source, excited by a pulse generator have been observed. Various distributions (Poisson, binomial and Polya) were used for the determination of the theoretical counting efficiency in both cases. The Poisson law gave a good result in the case of the LED but the Polya law had to be applied in the case of 55Fe. The results were independent of the scintillator volume. It seems that the validity of the Polya law in the case of LS-sources is related to the scintillator itself. Measurements of the 3H solution confirmed that conclusion.

Algorithms↗

Lorenz curves and their use in describing the distribution of 'the total burden' of dental caries in a population.

PURPOSE: 1) to describe the distribution of the total burden of dental caries in Danish adolescents over a 15-year period using Lorenz curves and, 2) to compare the observed distributions with Poisson distributions. METHOD: caries data for 15-year-old adolescents reported to the database for the national reporting system for the Danish Municipal Dental Service for Children and Adolescents in 1980 (n = 61,621) and 1995 (n = 50,359). RESULTS: The DMFS cut-off point for a given percentile had decreased from 1980 to 1995 and Lorenz curves showed a pattern of increasing inequality, even when only diseased individuals (i.e. with DMFS > or = 1) were included. The dispersion was larger than could be expected, if caries developed according to a random pattern modelled by e.g. a Poisson distribution. CONCLUSIONS: Lorenz curves may be a useful tool in the analysis of caries data, with special reference to determining the appropriateness of implementing high-risk preventive strategies.

Adolescent↗

A simple method to calculate the confidence interval of a standardized mortality ratio (SMR)

In analyzing standardized mortality ratios (SMRs), it is of interest to calculate a confidence interval for the true SMR. The exact limits of a specific interval can be obtained by means of the Poisson distribution either within an iterative procedure or by one of the tables. The limits can be approximated in using one of various shortcut methods. In this paper, a method is described for calculating the exact limits in a simple and easy way. The method is based on the link between the chi 2 distribution and the Poisson distribution. Only a table of the chi 2 distribution is necessary.

Confidence Intervals↗

Methodological issues in the development of the Canadian Cancer Incidence Atlas.

The Canadian Cancer Incidence Atlas is among recent national atlases using incidence rather than mortality data. Methods used to assess the significance and spatial correlation of the age-standardized rates (ASIRs) for the 290 census divisions are described. The expected number of cases by area was used to determine cancer sites with sufficient cases to be mapped. ASIR significance was assessed using a simulation based on a Poisson distribution. The consistency of the observed case distributions with the Poisson distribution was examined. The bootstrap confidence interval (CI) for the ASIR developed by Swift was used in the atlas. Spatial correlation was assessed with Moran's I/I(max) and the significance determined by a simulation in order to allow for area population variation. Data quality indicators typically used for cancer registries were presented, supplemented by a registry questionnaire.

Atlases as Topic↗

Cooperativity can reduce stochasticity in intracellular calcium dynamics.

The opening of inositol (1,4,5)-triphosphate (IP(3)) receptors, clustered at discrete sites on the endoplasmic reticulum, can lead to large-scale intracellular calcium waves. Recent experiments in Xenopus oocytes have shown that the inter-wave intervals for these waves have a standard deviation that is much smaller than their mean and that the background calcium concentration exhibits a slow rise during the interwave interval. Using a simple mathematical model, we examine the possibility that this slow rise increases the cooperativity between the openings of the clusters. We find that our model, coupled to the usual assumption that the pumps on the endoplasmic reticulum are activated instantaneously, is unable to explain the observed data: the clusters are found to fire independently and the inter-wave interval distribution is a Poisson distribution with a standard deviation that is approximately equal to its mean. On the other hand, we find that incorporating pumps that slowly activate leads to a slow increase in the background calcium concentration which makes global events progressively more likely to occur. We show that this cooperativity results in much smaller standard deviations and inter-wave interval distributions that are clearly not Poisson distributions.

Animals↗

[An analysis of the cellular distribution of chromosome aberrations induced in human lymphocytes after a single irradiation and under conditions of preliminary adaptive exposure].

Irradiation by an adaptive dose 0.05 Gy at the G0 stage decreased the number of chromosome aberrations induced in lymphocytes by a challenge dose 0.5 Gy at the G2 stage. Adaptive response was not observed at the G1 stage, when the cells were exposed to adaptive dose 0.05 Gy and challenge dose 1.0 Gy respectively after 24 h and 29 h incubation with PHA. In lymphocytes exposed to 1.0 Gy at the G1 stage, cellular distribution of chromosomal aberrations followed the Poisson distribution, while in lymphocytes exposed to 0.5 Gy at the G2 stage, the distribution of aberrations differed from the Poisson distribution and was nearer to the degenerated Poisson distribution. The adaptive dose 0.05 Gy did not alter the distribution of chromosome aberrations induced by the challenge dose at the G1 or the G2 stages. The role of independent and whole-cellular repair in the formation of chromosome and chromatid aberration is discussed.

Adaptation, Physiological↗

Distribution of spontaneous mutants and inferences about the replication mode of the RNA bacteriophage phi6.

When a parent virus replicates inside its host, it must first use its own genome as the template for replication. However, once progeny genomes are produced, the progeny can in turn act as templates. Depending on whether the progeny genomes become templates, the distribution of mutants produced by an infection varies greatly. While information on the distribution is important for many population genetic models, it is also useful for inferring the replication mode of a virus. We have analyzed the distribution of mutants emerging from single bursts in the RNA bacteriophage phi6 and find that the distribution closely matches a Poisson distribution. The match suggests that replication in this bacteriophage is effectively by a stamping machine model in which the parental genome is the main template used for replication. However, because the distribution deviates slightly from a Poisson distribution, the stamping machine is not perfect and some progeny genomes must replicate. By fitting our data to a replication model in which the progeny genomes become replicative at a given rate or probability per round of replication, we estimated the rate to be very low and on the on the order of 10(-4). We discuss whether different replication modes may confer an adaptive advantage to viruses.

Bacteriophage phi 6↗

[Current aspects on evaluation of assays of factor-VIII activity, factor-VIII associated protein and factor-VIII neutralizing antibody (author's transl)].

In evaluating factor-VIII activity it should be noted that regarding the remaining activity of deficient plasma a linear reference curve is achieved. In the standard population factor-VIII activity and factor-VIII associated protein are distributed approximately lognormally. Due to this distribution certain results have been gained for the optimal choice of localisation and dispersion measures. It is assumed that the proportions of neutralized factor-VIII activity in plasma are distributed according to Poisson. The applicability of the Poisson distribution was also proved for the free factor-VIII activity portion. Due to the Poisson distribution the antibody unit is clearly defined, thus eliminating a further discussion on the establishment of an arbitrary standardized antibody unit.

Antibodies↗

Fitting discrete probability distributions to evolutionary events.

The assumptions underlying the use of the Poisson distribution are essentially that the probability of an event is small but nearly identical for all occurrences and that the occurrence of an event does not alter the probability of recurrence of such events. These assumptions do not seem to be met for evolutionary events since (i) the probability of fixing nucleotide codon substitutions is not equal for all substitutions at a codon, and probably varies for the same substitution in different lineages; (ii) the probability of fixing codon substitutions varies among positions of a cistron; and (iii) the fixation of a nucleotide codon substitution at one position in a cistron modifies, and may even promote, the fixation of a codon substitution elsewhere along the cistron. Natural selection presumably is the causative factor that acts to modify the probability of a nucleotide codon substitution's being fixed in a population. The use of the negative binomial distribution is consistent with the evidence that selective pressure on amino acid or nucleotide codon positions varies both among codon positions of a cistron and at a particular position during evolutionary time. If the number of fixations of nucleotide codon substitutions per position of cistrons encoding cytochromes c are phyletically inferred (phylogeny based on a paleontological record) rather than phenetically inferred (based on paired comparisons of extant species' differences in the absence of a phylogeny) the distribution of these fixation data cannot be described adequately by a single Poisson distribution. The fit of these same data to a negative binomial distribution is very satisfactory. It has been argued that the fit of phenetically inferred fixation data, which do not take account of parallel or reverse fixations, to the Poisson distribution was supportive evidence for the hypothesis that protein evolution results from the fixation of selectively neutral codon substitutions. This argument now appears to be undercut by the evidence that data on nucleotide codon fixation are more probably distributed according to the negative binomial distribution. The fact that fixation data can be described by a particular discrete probability distribution does not of itself provide insight into the mechanisms of the evolutionary process. However, the facts-(i) that the assumptions underlying the use of the negative binomial distribution adequately deal with the varying probability of fixing amino acid or nucleotide codon substitutions at and among the positions of a cistron and (ii) that the negative binomial distribution provides an excellent fit for the phyletically inferred fixation data-suggest that the negative binomial is a very appropriate discrete probability distribution for describing evolutionary events. Amino acids or their nucleotide codon substitutions may be fixed at a position of a cistron as though selectively neutral relative to the codon being replaced, even though the codon position will not be selectively neutral, since many amino acids cannot function there. The negative binomial distribution treats this situation well whereas a single Poisson distribution could only be satisfactory if all codon positions that could vary were selectively neutral.

Amino Acid Sequence↗

Temporal patterns of atrial arrhythmia recurrences in patients with implantable defibrillators: implications for assessing antiarrhythmic therapies.

INTRODUCTION: The statistical measures commonly used to assess therapies for recurrent atrial arrhythmias (such as time to first recurrence) often assume a uniformly random pattern of arrhythmic events over time. However, the true temporal pattern of atrial arrhythmia recurrences is unknown. The aim of this study was to use linear and nonlinear analyses to characterize the temporal pattern of atrial arrhythmia recurrences in patients with implantable cardioverter defibrillators. METHODS AND RESULTS: The time and date of atrial tachyarrhythmias recorded in 65 patients with combined atrial and ventricular defibrillators were used to construct a probability density function (PDF) and a model of a Poisson distribution of arrhythmic events for each patient. Average patient age was 66 +/- 10 years and follow-up was 7.8 +/- 4.8 months. A total of 10,759 episodes of atrial tachyarrhythmias were analyzed (range 43 to 618 episodes per patient). The PDF fit a power law distribution for all 65 patients, with an average r2 = 0.89 +/- 0.08. The PDF distribution differed significantly from the model Poisson distribution in 47 of 65 patients (P = 0.0002). Differences from the Poisson distribution were noted for patients both taking (30/43 patients; P < or = 0.015) and not taking (17/22 patients; P < or = 0.017) antiarrhythmic drugs. Median time between atrial arrhythmia detections for all 65 patients was 10.8 minutes. CONCLUSION: In implantable cardioverter defibrillator patients, the temporal pattern of frequent recurrences of atrial tachyarrhythmias usually is characterized by a power law distribution. The unique statistical properties of this type of distribution should be considered in designing outcome measures for treatment of atrial tachyarrhythmias.

Adult↗

A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives.

Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives.

Animals↗

A simple statistical approach that represents the frequency distribution of plasmids in clinical isolates of the enterobacteria.

The frequency distribution of plasmids in a representative collection of Escherichia coli and other enterobacteria was compared with the frequencies predicted by the Poisson distribution. The distribution of E. coli plasmids did not differ significantly (p greater than 0.2) whereas the difference between observed and predicted distributions of plasmids in combined populations of other enterobacteria was significant (p less than 0.001). Previous studies had suggested that plasmid-free strains contributed disproportionately to the overall frequency distribution. Therefore, plasmid-free strains were excluded and the frequency distribution of plasmids in plasmid-containing strains compared with frequencies predicted by a modified Poisson distribution conditional upon n not equal to 0. The results obtained showed that the frequency distribution of plasmids in E. coli and in other enterobacteria did not differ significantly from the predicted distribution (p less than 0.2 and p greater than 0.6 respectively). The frequency distribution of plasmids in previously published studies was compared with predicted frequencies by means of the Poisson distribution and the modified Poisson distribution conditional upon n not equal to 0. The results indicate that the modified Poisson distribution described provides an adequate description of plasmid frequency distributions and represents the observed frequencies better than the distribution predicted directly from the Poisson formula.

Enterobacteriaceae↗

Evaluation of the bias in using the time to the first event when the inter-event intervals have a Weibull distribution.

Currently the analysis of clinical trials for treatment of paroxysmal atrial fibrillation (PAF) relies on the assumption that the events are distributed according to a Poisson distribution. We contend that the occurrence of PAF events are clearly not Poisson and tend to occur in clusters. A candidate parametric model of the inter-event interval, the Weibull distribution, is presented. When the events are distributed according to a Poisson distribution, the time to the first event (TFE) has the same distribution as the inter-event intervals (IEI) due to the 'memoryless' property of the Poisson distribution, hence the TFE can be used instead of the IEI. When the events do not form a Poisson distribution, the TFE does not have the same distribution as the IEI. We show that for the Weibull distribution, when the TFE is used to model the IEI, both the mean and the survivor distribution are biased. The bias in the survivor function is a function both of time and the parameters of the distribution. Therefore when two groups have different parameters for their distributions (as in the case of different treatment effects), the discrepancy between the survivor distribution of the IEI and the survivor distribution of the TFE is affected differentially. We demonstrate the low coverage probabilities of the mean and the survivor function which result when the underlying distribution is Weibull with shape parameter kappa < 1.0. It is likely that this problem will arise for other clustered event processes. This suggests that careful empirical investigation of the distribution of IEI for recurrent events is necessary before choosing to analyse the data using the TFE.

Atrial Fibrillation↗

The significance of leukemia and lymphoma cells in cerebrospinal fluid contaminated by blood containing malignant cells: a probabilistic approach based on the Poisson frequency distribution.

The significance of malignant cells in a body fluid is often difficult to determine if that fluid is contaminated by blood containing malignant cells. This problem is most often seen in examination of CSF from patients with lymphoma or leukemia. We suggest a statistical model of this problem in which the numbers of malignant cells in the blood and the fluid specimen are related to the number of red blood cells. Using the Poisson distribution, the probability of finding the observed number of malignant cells in the fluid is calculated and used as the basis for suggesting whether these cells are likely to represent contamination effect or true involvement of the fluid by the malignancy. The limitations and applicability of this process are discussed.

Blood Cells↗

Estimating random errors due to shot noise in backscatter lidar observations.

We discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson- distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root mean square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF, uncertainties can be reliably calculated from or for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations lidar and tested using data from the Lidar In-space Technology Experiment.

Journal Article↗

[Mortality rate and its statistical properties].

The rate is an epidemiologic measure which has a widespread use in describing the occurrence of diseases. In this paper, with a didactic approach, the definition of the mortality (morbidity) rate is introduced following two ways of reasoning: firstly, in the context of survival analysis, as an instantaneous conditional probability of failure (either disease or death) (instantaneous risk) and, secondly, as a traditional measure of rapidity of change in time. We then proceed to highlight the differences, in terms of definition, interpretation, and application, between the concepts of rate and risk. As a next step the statistical properties of the rate are explored and it is explained why the variability of the measure is simply associated with the numerator (events) and not with the denominator (person-times) of the rate. In this context the Poisson distribution is commonly considered the probability distribution which better describes the statistical variability of the observed events, and examples of such a distribution are presented. When the number of deaths is sufficiently elevated the Poisson distribution can be adequately approximated by the Gauss distribution, which is simpler and in common use in occupational medicine, and formulas are presented to compute mean and variance of the rate in this situation. When the number of deaths is small a suggestion is made of making a log transformation of the rate (or of the deaths) before using the Gauss distribution: formulas are proposed for this situation, too. As a practical application of the statistical properties presented and as a concluding example, a confidence interval for the rate is computed. Numerical and graphical comparisons of the results deriving from the use of different formulas are described.

Confidence Intervals↗