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Photon statistics of random lasers with resonant feedback.

We have measured the photon statistics of random lasers with resonant feedback. With an increase of the pump intensity, the photon number distribution in a single mode changes continuously from Bose-Einstein distribution at the threshold to Poisson distribution well above the threshold. The second-order correlation coefficient drops gradually from 2 to 1. By comparing the photon statistics of a random laser with resonant feedback and that of a random laser with nonresonant feedback, we illustrate very different lasing mechanisms for the two types of random lasers.

Journal Article↗

Counting every quantum.

1. Human subjects were asked to rate both blanks and very dim flashes of light under conditions of complete dark adaptation at 7 degrees in the periphery. The ratings used were 0, 1, 2, 3, 4, 5, and 6.2. For one subject (B.S.) the distributions of ratings were approximately Poisson distributions. The data were consistent with each rating being the actual number of effective quantal absorptions plus the number of noise events. This subject was presumably able to count every rod signal (effective absorptions plus noise).3. For two other subjects, the data were consistent with the ratings being one less (L.F.) and two less (K.D.) than the number of effective absorptions plus noise. They were able to count every rod signal beginning with 2 and 3 respectively. A fourth subject's erratic data could not be fitted.4. The fraction of quanta incident at the cornea that resulted in a rod signal was estimated to be about 0.03 which is consistent with physical estimates of effective absorption for that retinal region.5. A simulated forced choice experiment leads to an absolute threshold about 0.40 log units below the normal yes-no absolute threshold. This and other results indicate that subjects can use the sensory information they receive even when only 1, 2 or 3 quanta are effectively absorbed, depending on the individual. Humans may be able to count every action potential or every discrete burst of action potentials in some critical neurone.

Dark Adaptation↗

Single photon signals in fly photoreceptors and first order interneurones at behavioral threshold.

1. The contrast sensitivity of the optomotor response of the fly Musca domestica was measured using a moving sinusoidal grating as the stimulus. In parallel experiments intracellular recordings were made from photoreceptors and first order visual interneurones to to determine their responses to the same threshold stimuli. Measurements of the spatial modulation transfer function for photoreceptors confirm that the optics of the eye were intact during recordings. 2. At the lowest intensity at which one can obtain an optomotor response, the photoreceptor signal is a train of discrete depolarizations, or bumps. With constant intensity stimuli, the temporal distribution of bumps followed the Poisson distribution with a mean rate of proportional to luminance. The mean bump rate at the threshold intensity for a behavioural response is 1.7 +/- 0.7 s-1 (mean +/- S.D., n = 25). 3. Calibrations and the statistical properties of the bump train indicate that a bump represents one effective photon, implying that the bump : photon ratios are quantum capture efficiencies. 4. At low intensities the first order interneurones (the large monopolar cells or LMCs) show hyperpolarizing bumps each triggered by a receptor bump. Using a point source stimulus, centred in the field of view, the LMC bump rate is six times that in a single receptor viewing the same stimulus, as expected from the known projection of six receptor axons to each LMC. When using an extended stimulus (the grating), the bump rate is 18-20 times that in receptors. Comparison with earlier work suggests that this increased lateral summation of receptor inputs to LMCs only occurs at very low intensities. 5. In both receptor and LMCs the amplitudes and wave forms of bumps depend upon the position of a point source stimulus within the field of view. With the light in the periphery of the field the bumps are smaller and slower than when the light is in the centre. This difference in response suggests that spatial stimulation is brought about by lateral interactions, possibly between receptors. 6. At higher mean intensities the signal-to-noise ratios in receptors responding to the appropriate threshold stimuli increase with intensity. This is suggestive of a decrease in the extent of spatial and/or temporal summation in the optomotor pathway.

Action Potentials↗

Dose dependency of FISH-detected translocations in stable and unstable cells after Cs gamma irradiation of human lymphocytes in vitro.

Human peripheral lymphocytes were exposed to 137Cs gamma-rays (0-4.3 Gy) in order to check the impact of unstable cells on the dose-response curve for translocations. Chromosomes 2, 4 and 8 were FISH-painted. 17,720 first dividing cells were analysed. For the discrimination between stable and unstable cells the painted and the counter-stained chromosomes were analysed at doses of 1 Gy and higher. The cell distribution of translocations follows a Poisson distribution. The data were fitted to the linear-quadratic function, y = c + alphaD + betaD2. As expected, the alpha coefficients of the dose-response curves for translocations in stable cells or in total cells do not differ. However, at doses >1 Gy, the frequency of all translocations in stable cells seems to be lower than the frequency in total cells. For the establishment of calibration curves for past dose assessment purposes, only complete translocations should be scored, in order to estimate reliable doses.

Algorithms↗

The genetic structure of recombinant inbred mice: high-resolution consensus maps for complex trait analysis.

BACKGROUND: Recombinant inbred (RI) strains of mice are an important resource used to map and analyze complex traits. They have proved particularly effective in multidisciplinary genetic studies. Widespread use of RI strains has been hampered by their modest numbers and by the difficulty of combining results derived from different RI sets. RESULTS: We have increased the density of typed microsatellite markers two- to five-fold in each of several major RI sets that share C57BL/6 as a parental strain (AXB, BXA, BXD, BXH and CXB). A common set of 490 markers was genotyped in just over 100 RI strains. Genotypes of around 1,100 additional microsatellites in one or more RI sets were generated, collected and checked for errors. Consensus RI maps that integrate genotypes of approximately 1,600 microsatellite loci were assembled. The genomes of individual strains typically incorporate 45-55 recombination breakpoints. The collected RI set - termed the BXN set - contains approximately 5,000 breakpoints. The distribution of recombinations approximates a Poisson distribution and distances between breakpoints average about 0.5 centimorgans (cM). Locations of most breakpoints have been defined with a precision of < 2 cM. Genotypes deviate from Hardy-Weinberg equilibrium in only a small number of intervals. CONCLUSIONS: Consensus maps derived from RI strains conform almost exactly to theoretical expectation and are close to the length predicted by the Haldane-Waddington equation (x3.6 for a 2-3 cM interval between markers). Non-syntenic associations between different chromosomes introduce predictable distortions in quantitative trait locus (QTL) datasets that can be partly corrected using two-locus correlation matrices.

Alleles↗

Sister chromatid exchange in chromosomes of sheep (Ovis aries).

Blood lymphocyte cultures from 32 Comisana and Laticauda sheep breeds (15 males and 17 females) raised in Southern Italy were studied using sister chromatid exchange (SCE) test. Of the 932 cells studied, the SCE-mean value was 7.20 +/- 2.5 per cell for both breeds. Indeed, the SCE mean values were 7.12 +/- 2.45 and 7.28 +/- 2.55 in Comisana and Laticauda breeds, respectively, and the differences were not significant. No statistical differences were noticed between male and female cells (7.25 +/- 2.39 and 7.16 +/- 2.60, respectively). The SCE frequency distribution did not follow a Poisson distribution. The number of SCE were significantly higher than expected in chromosomes 1, 2 and 3 (p < 0.001) and significantly lower than expected in the X and remaining chromosomes (p < 0.001) on the basis of relative chromosome lengths.

Animals↗

Microdosimetry and chromosome aberrations: effects of 230 keV neutrons on Vicia faba chromosomes.

Physical energy deposition events have been related to sub-nuclear cytological events (chromosomal changes) in metaphases sequentially accumulated from the latter part of the cell cycle of Vicia faba. 230 keV neutrons produce about 0.4 recoil protons per late interphase nucleus per rad with the majority of protons traveling 1 to 2 microns from their origin, depositing energy at around 90 keV per micron. The frequency of induced abberrations is basically linear with dose, though varying through consecutive cell sampling periods because of differential induced mitotic delay. Distributions of chromosomal aberrations and total cytological events are overdispersed in relation to the Poisson distribution indicating that some proton recoils produce multiple events. When gaps and aberrations within chromosomes and multiple aberrations between chromosomes, are considered as discrete events, distributions follow Poisson expectations. About 40% of proton recoils result in observable cytological change. The highly energetic proton recoils (approximately 90 keV per micron) which can induce multiple events are the ones most likely to produce effects which result in cell death. The sphere of influence of the proton recoils is probably adequately estimated from their range (approximately 1 to 2 micron) since it seems compatible with the spatial proximity of the initial components of the resultant chromosome aberrations.

Chromosome Aberrations↗

Seizure frequency in intractable partial epilepsy: a statistical analysis.

We examined the seizure records of 13 patients (nine men and four women, ages 27-50 years) with intractable partial epilepsy, maintained with steady anti-epileptic drug dosages. Patients recorded daily seizure frequency on calendars. Periods of outpatient observation ranged from 99 to 1,710 days and the number of observed seizures ranged from 18 to over 400, with daily seizure rates of 0.1-4.3 per day. We used the quasi-likelihood regression model to examine the following four departures of the daily seizure counts from a Poisson (random) model: (1) linear increasing or decreasing time trends in expected seizure rates; (2) clustering, where the expected seizure rate on a given day depends on the number of seizures observed on the immediate prior days; (3) monthly cyclicity; and (4) increased variability (overdispersion). Linear time trends were seen in six patients (four increasing and two decreasing), clustering was seen in 10 patients, and a near-monthly cycle appeared in four patients (two of nine men and two of four women). A significant amount of extra variation (overdispersion) relative to a Poisson distribution was observed in all but one of the 13 patients. Departures from a Poisson (random) model appear more common in this population of patients with medically intractable epilepsy than is commonly recognized, and have clinical importance as well as implications for the design of clinical studies.

Adult↗

Count-rate statistics of the gamma camera.

The temporal distribution of decay events recorded by a gamma camera in 'list mode' differs from the Poisson distribution because of dead-time effects. We propose a new model for the dead-time behaviour of a gamma camera. The most important feature of our model is that the loss of events occurs in pairs or higher multiples due to the so-called 'pile-up' effect. We analyse the consequences of pile-up for the temporal distribution of events recorded by a gamma camera. The probability distribution for the time intervals between events recorded by the camera is calculated from first principles. We construct estimators for the parameter of the new distribution. We distinguish between the estimation of the total count rate and the estimation of a certain subset of the total count rate. Computer simulation confirms that our estimators are less influenced by dead-time effects than the standard estimator.

Computer Simulation↗

[Radiation damages in human lymphocytes studied by micronucleus and chromosomal analysis].

It was shown that the dependence of the micronucleus number and chromosome aberration on irradiation dose is linear quadratic, the values of linear coefficient being different. The distribution of ameliorators and children from the areas with higher irradiation level by micronucleus test conforms to Poisson distribution, while the distribution by chromosomal analysis approaches to binomial distribution.

Adult↗

Sample size calculations for single group post-marketing cohort studies.

In pharmacoepidemiology, single group cohort is the most frequently proposed design to determine if the incidence rate of an adverse drug reaction among the exposed differs from a reference value. In many situations, the number of events expected in the cohort is too small to conduct sample size calculations based on the normal distribution. This paper proposes, for a single group cohort study, calculations and tables derived from the Poisson distribution. The results are based on a one-sided test with a 0.05 significance level and a power of 0.9 and 0.8. Two parameters have to be specified a priori: the expected incidence of the event under the null hypothesis and the minimum risk ratio to be detected. The required sample size and the critical number of events to reject the null hypothesis are directly derived from the tables. Results show that the normal approximation may lead to an underestimation of the required sample size.

Cohort Studies↗

Multi-target models and their application to data analysis of cellular mortality due to radiation exposure.

We consider multi-target models for use in analyzing data of the dose-response relationship. The target sizes we are concerned with here are both homogeneous, as assumed in the classical model, and heterogeneous, as simplified using geometric progression. We apply two models for establishing the multi-target models: a Poisson regression model constructed by assuming that the response variable Y follows Poisson distribution, and a gamma-frailty model as a Poisson mixture model derived by adding random common risks having a gamma distribution. Applying these models to experimental data relating the effects of miso fermentation-stages on the survival rate of cells of intestinal crypts of mice exposed to radiation yielded the result that there were substantial frailties associated with all miso fermentation-stages. Short-term and medium-term fermented miso provided similar effects, whereas long-term fermentation had the lowest-relative risk value, indicating a significant protection of the crypts against exposure effects. A gamma-frailty model based on heterogeneous target size was more suitably applied when there were at least 3 dead stem cells having 10 target genes.

Animals↗

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.

Animals↗

Population dynamics: Poisson approximation and its relation to the Langevin process.

We discuss how to simulate a stochastic evolution process in terms of difference equations with Poisson distributions of independent events when the problem is naturally described by discrete variables. For large populations the Poisson approximation becomes a discrete integration of the Langevin approximation [T. G. Kurtz, J. Appl. Prob. 7, 49 (1970); 8, 344 (1971)]. We analyze when the latter gives a reasonable representation of the original evolution for finite size systems. A simple example of an epidemic process is used to organize the discussion and to perform statistical tests that underline the goodness of the proposed method.

Poisson Distribution↗

The Ames test: the two-fold rule revisited.

Mutagenicity in the Ames assay is evaluated by comparing the number of revertants observed in treated cultures to those in untreated cultures. Often, some form of the '2-fold rule' is employed, whereby a compound is judged mutagenic if a 2-fold or greater increase is seen in a treated culture. In order to understand the underpinnings of this approach, we study some of its statistical properties. We assume that the number of revertants on any plate from a given two-group experiment follows a Poisson distribution and we address the following questions: (1) what is the false-positive error probability of observing at least a doubling of the number of colonies from the control to the treatment group?; (2) if a given mean number of colonies is postulated for a control group, what number of colonies above the observed control mean provides a false-positive rate of 5%? We also present results for question 1 in the case where the number of revertants follows a negative binomial distribution.

False Positive Reactions↗

A model for the neuronal implementation of selective visual attention based on temporal correlation among neurons.

We propose a model for the neuronal implementation of selective visual attention based on temporal correlation among groups of neurons. Neurons in primary visual cortex respond to visual stimuli with a Poisson distributed spike train with an appropriate, stimulus-dependent mean firing rate. The spike trains of neurons whose receptive fields do not overlap with the "focus of attention" are distributed according to homogeneous (time-independent) Poisson process with no correlation between action potentials of different neurons. In contrast, spike trains of neurons with receptive fields within the focus of attention are distributed according to non-homogeneous (time-dependent) Poisson processes. Since the short-term average spike rates of all neurons with receptive fields in the focus of attention covary, correlations between these spike trains are introduced which are detected by inhibitory interneurons in V4. These cells, modeled as modified integrate-and-fire neurons, function as coincidence detectors and suppress the response of V4 cells associated with non-attended visual stimuli. The model reproduces quantitatively experimental data obtained in cortical area V4 of monkey by Moran and Desimone (1985).

Animals↗

Monitoring tsetse fly populations. II. The effect of climate on trap catches of Glossina pallidipes.

In Part I it was shown that the sampling distribution of trap catches of tsetse flies, Glossina pallidipes Austen, at Nguruman, Kenya, using unbaited biconical traps follows a Poisson distribution. In this paper we examine the effect of humidity and temperature on day-to-day and seasonal variations in the trap catches. It is shown that the seasonal variation is significantly correlated with maximum daily temperature, the catches increasing with temperature when the maximum temperature is below 34 degrees C and decreasing with temperature when it is above 34 degrees C. The correlation between trap catches and relative humidity is not as good as the correlation with the maximum temperature, and the two together do not improve the fit to the trap catches. The day-to-day variation is significantly greater than the intrinsic variation due to the stochastic nature of the sampling process and for some traps it is correlated with temperature and humidity. An autoregressive model gives a half-life for the decay of departures from the mean of about 1 day and it is suggested that this indicates the movement of flies in response to animal movement or to climatic factors other than temperature or humidity. After removing the temperature dependent part of the seasonal variation and the autoregressive component of the data, the male and female catches are still significantly correlated.

Animals↗

Some goodness-of-fit methods for the Poisson plus added zeros distribution.

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.

Bacteria↗