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Sister chromatid exchange (SCE) were studied in 22 patients with breast cancer (i.e., four stage II; 12 stage III, six stage IV) and 10 normal healthy females as age-matched controls. The data obtained in these cases followed a Poisson distribution. An apparent increase in the average rate of SCE/cell was observed with the advancing stage of breast cancer.
Paraplegic subjects (N = 34) were examined to determine the association of pressure sore history with respect to ankle pressure ratio and buttocks cutaneous plethysmographic harmonic persistence. No relationship was found between pressure sore history and ankle pressure ratio. No significant difference in ankle pressure ratios exists for those who have a pressure sore history as compared to those who have not experienced a pressure sore in 5 years. Those subjects with a diminished buttocks circulation harmonic persistence are more likely to have experienced one or more pressure sores than those subjects with normal circulation characteristics. A Poisson distribution analysis of multiple pressure sore occurrence suggests that repeated pressure sores are unlikely to arise as the result of chance.
Data were collected on the distribution of nine families of transposable elements among second and third chromosomes isolated from a natural population of Drosophila melanogaster, by means of in situ hybridization of element probes to polytene chromosomes. It was found that the copy numbers per chromosome in the distal sections of the chromosome arms followed a Poisson distribution. Elements appeared to be distributed randomly along the distal sections of the chromosome arms. There was no evidence for linkage disequilibrium in the distal sections of the chromosomes, but some significant disequilibrium was detected in proximal regions. There were many significant correlations between different element families with respect to the identity of the sites that were occupied in the sample. There were also significant correlations between families with respect to sites at which elements achieved relatively high frequencies. Element frequencies per chromosome band were generally low in the distal sections, but were higher proximally. These results are discussed in the light of models of the population dynamics of transposable elements. It is concluded that they provide strong evidence for the operation of a force or forces opposing transpositional increase in copy number. The data suggest that the rate of transposition per element per generation is of the order of 10(-4), for the elements included in this study.
Neyman-Pearson principles are briefly discussed and 95% confidence intervals of the form [0, ##.##] are presented. Use is made of the fact that the probability of the difference of two random variables, each with a Poisson distribution, can be expressed in terms of modified Bessel functions of integral order and elementary functions. The validity of the values is discussed.
The selectivity for temporal characteristics of sound and interaural time difference (ITD) was investigated in the torus semicircularis (TS) of the grassfrog. Stimuli were delivered by means of a closed sound system and consisted of binaurally presented Poisson distributed condensation clicks, and pseudo-random (RAN) or equidistant (EQU) click trains of which ITD was varied. With RAN and EQU trains, 86% of the TS units demonstrated a clear selectivity for ITD. Most commonly, these units had monotonically increasing ITD-rate functions. In general, units responding to Poisson clicks, responded also to RAN and EQU trains. One category of units which showed strong time-locking had comparable selectivities for ITD with both stimulus ensembles. A second category of units showed a combined selectivity for temporal structure and ITD. These units responded exclusively to EQU trains in a nonsynchronized way. From the responses obtained with the Poisson click ensemble so-called Poisson system kernels were determined, in analogy to the Wiener-Volterra functional expansion for nonlinear systems. The kernel analysis was performed up to second order. Contralateral (CL) first order kernels usually had positive or combinations of positive and negative regions, indicating that the contralateral ear exerted an excitatory or combined excitatory-inhibitory influence upon the neural response. Ipsilateral (IL), units were characterized by first order kernels which were not significantly different from zero, or kernels in which a single negative region was present. A large variety of CL second order kernels has been observed whereas rarely IL second order kernels were encountered. About 35% of the units possessed nonzero second order cross kernels, which indicates that CL and IL neural processes are interacting in a nonlinear way. Units demonstrating a pronounced selectivity for ITD, were generally characterized by positive CL combined with negative IL first order kernels. Findings suggested that, in the grassfrog, neural selectivity for ITD mainly is established by linear interaction of excitatory and inhibitory processes originating from the CL and IL ear, respectively. Units exhibiting strong time-locking to Poisson clicks and RAN and EQU trains had significantly shorter response latencies than moderately time-locking units. In the first category of units, a substantial higher number of nonzero first and second order kernels was observed. It was concluded that nonlinear response properties, as observed in TS units, most likely have to be ascribed to nonlinear characteristics of neural components located in the auditory nervous system peripheral to the torus semicircularis.
The authors present algorithms to compute the confidence interval for a Poisson parameter (lambda) and the p value for testing the hypothesis that lambda is equal to a constant, which can be used to make inferences about the standardized mortality ratio and the standardized incidence ratio. The p value and confidence interval always agree, despite the discrete nature of the Poisson distribution. The authors also give simple equations to compute numeric approximations of the confidence limits that do not require the use of any probability distributions. An example based on data arising from a study of cancer incidence is given.
A major problem in epileptology is why a seizure occurs at a particular moment in time. An initial step in solving this problem is a detailed analysis of the temporal distribution of seizures. Using methods and theories of stochastic processes, seizure patterns in a group of epileptic outpatients were examined for stationarity, randomness, dependency and periodicity in a prospective study. Sixteen of the 21 seizure diaries included in the study showed stationarity; 2 were non-stationary and 3 inconclusive. Eleven of the 16 stationary diaries were non-Poisson (P less than 0.005), indicating that in the majority of patients seizures did not occur randomly. The most frequently encountered phenomenon was seizure clustering. Clustering was considered when the diaries fulfilled all three criteria: (1) a positive R-test (P less than 0.001); (2) deviation from the fitted Poisson distribution towards clustering; and (3) the feature of an autoregressive process in the autocorrelogram plot. Dependency between seizure events was demonstrated in 8 of the 16 stationary diaries, computing first order transition probabilities. A detailed analysis of seizure occurrence is a major step towards a better understanding of the mechanisms underlying seizure precipitation. This is exemplified by our finding of a relation between seizure frequency and the menstrual cycle.
An HMX/insulin two-layer system was chosen as a model for further investigation of the matrix properties of explosive materials for protein analytes in plasma desorption mass spectrometry. The dependencies of the molecular ion yield and average charge state as a function of the analyte thickness were studied. An increase in the charge state of multiply protonated molecular species was confirmed as the major matrix effect, with the average charge state z at the smallest thickness studied being higher than in matrix-assisted laser desorption/ionization and closer to the value obtained in electrospray ionization under standard acidic conditions. Observed charge state distributions are significantly narrower than the corresponding Poisson distributions, which suggests that the protonation of insulin is limited in plasma desorption by the number of basic sites in the molecule, similar to electrospray ionization. Both the curve displaying total molecular ion yield and the one showing the total charge (proton) yield as a function of the insulin thickness have maxima at a thickness different from an insulin monolayer. These observations diminish the significance of a matrix/analyte interface mechanism for the explosive matrix assistance. Instead, a mechanism related to the chemical energy release during conversion of the explosive after the ion impact is proposed. As additional mechanisms, enhanced protonation of the analyte through collisions with products of the explosive decay is considered, as well as electron scavenging by other products, which leads to a higher survival probability of positively charged protein molecular ions. Copyright 1999 John Wiley & Sons, Ltd.
Frequencies of voiding and urinary incontinence are commonly measured by a patient's recall or a diary. The recommended diary length varies from 1 to 14 days, with 7 days apparently being most common. To examine the statistical precision of these different modalities, we analyzed recall data and diary data of 74 patients with urinary frequency, incontinence, or both. Recall data on voiding and incontinence frequency were systematically higher and more variable than diary data. Longer diary length provided less variable diary data. The confidence interval of diary data was calculated by applying the normal distribution to daytime voiding frequency and the Poisson distribution to daytime incontinence frequency. For daytime voiding frequency, the 95% confidence interval was estimated to be (x - 2.65, x + 2.65) (x - 1.53, x + 1.53) (x - 1, x + 1), where x is the 1-day, 3-day, and 7-day diary mean, respectively. For daytime incontinence frequency, the confidence interval depended on both the diary length and the diary mean. It was estimated to be (0, 6.39), (1.72, 4.28), (2.36, 3.64), by using a diary mean of 3 or 1-day, 7-day, and 28-day diaries, respectively. Also, it was estimated to be (0, 1.02), (1.72, 4.28), (7.66, 12.34), when the 7-day diary mean was 0.5, 3, and 10, respectively. Studies with different samples of genuine stress incontinence (n = 37) and urge incontinence (n = 25) confirmed these results. In conclusion, we believe the 7-day diary is highly reliable for estimating voiding frequency and is a reasonable option for predicting incontinence episodes. However, the diary length should be extended in a patient with rarer events of incontinence, and it should be shortened for those who are incontinent more often or who are diagnosed with voiding frequency only.
A simple and reliable statistical method is proposed to distinguish real fragile sites from the casual accumulation of aberrations that can occur as a consequence of random distribution. It is based on a study of the expected random distribution, assumed to be equal to a Poisson distribution, with the expected value of events per band as the mean.
Differences in axosomatic synapses between GABA-accumulating [G(+)N] or non-accumulating [G(-)N] neurons have been investigated in the visual cortex of adult rat. The neurons were classified and localized in light microscopic autoradiograms after [3H]GABA injections. The cells resectioned for electron microscopic identification of type 1 synapses (T1S) and type 2 synapses (T2S). A total of 167 neurons [45 G(+)N, 122 G(-)N] situated in laminae II-VI were evaluated. The two groups of neurons were not uniform populations. G(-)N included both pyramidal and non-pyramidal neurons, whereas no typical pyramidal neurons were found among G(+)N. A total of 691 synaptic contacts was evaluated for these groups of somata. The density of synapses was higher on G(+)N than on G(-)N. This was mainly due to a difference in the number of T1S. On G(-)N the frequency distributions of both types of synapses represented Poisson distributions, indicating that there were stochastic variations around mean values. In contrast, on G(+)N the distribution was exponential which suggests that G(+)N include several subpopulations with different densities of T1S. On all cortical neurons the average density of T2S was 509-60 T2S per 1000 microns2 of soma surface, which resembles the density in the neuropil. In contrast, T1S varied from zero to a mean of 12 per 1000 microns2 on G(-)N and to a mean of 51 per 1000 microns2 on G(+)N, i.e. the density of T1S, unlike T2S, is much smaller on neuronal somata than in the surrounding neuropil. It is suggested that the formation of axosomatic T1S, but not of T2S, is suppressed to a variable degree on almost all cortical neurons. Only on pyramidal neurons does the suppression of T1S seem to be complete.
Development of the procedure to stimulate peripheral blood lymphocytes has greatly facilitated the understanding of chromosome aberration formation and repair mechanisms in human cells. Yet, because radiation induces far more initial chromosome breaks than are observed as aberrations in metaphase, it has not been possible to examine the kinetics of primary chromosome breakage and rejoining with this procedure. An improved method to induce premature chromosome condensation in unstimulated lymphocytes has been used to study primary chromosome breakage, rejoining, and ring formation at various times after irradiation with up to 800 rad of X-rays. The dose-response relations for chromosome fragments analyzed immediately or 1, 2, or 24 h after exposure were found to be linear. Rapid rejoining of chromosome fragments, which takes place in the first 3 h after X-ray exposure, was not correlated with a simultaneous increase in the formation of rings. The yield of rings per cell scored 24 h after irradiation, however, increased significantly and fit a linear quadratic equation. Both chromosome fragment rejoining and ring formation were completed about 6 h after irradiation. The frequency distributions of rings among cells followed a Poisson distribution, whereas chromosome fragments were overdispersed.
Human blood was irradiated with beta-particles from an external source of 90Sr. The source was a rolled piece of silver foil, active dimensions: 100 X 12.5 mm, incorporating 3.7 X 10(8) Bq (10 mCi) of 90Sr/90Y. After culturing for 48 h, the dicentric yield in the lymphocytes at the first metaphase was measured as a function of the dose in the blood. The aberration yield fitted the linear-quadratic function well, which is consistent with the single-track and two-track model for aberration formation at low LET radiation. The curve for 90Sr beta-rays was compared with a curve for 60Co gamma-rays. The main difference between the coefficients was in the alpha values. With respect to 60Co gamma-rays, the RBE calculated from the dose-effect relationships for dicentric production was 2.8 at the dose of 0.14 Gy; it decreased with increasing doses. The distribution of dicentrics was consistent with the Poisson distribution but showed a tendency to over-dispersion in the region of higher doses. A reason for these discrepancies is discussed.
Here we compared the effectiveness of neutrons ( = 5.5 MeV) versus 60Co gamma-rays in producing micronuclei (MN) in human lymphocytes. To obtain dose-response data, blood samples of six donors were irradiated with doses ranging from 0.1 to 5 Gy for gamma-rays and 0.1-3 Gy for neutrons. A linear dependence of MN yield with dose was found for fast neutrons while for gamma-rays a nonlinear dependence existed. For both radiation qualities no significant interindividual differences were found. Derived relative biological effectiveness values decreased with increasing dose. The MN frequency distributions were overdispersed with respect to the Poisson distribution, with neutrons showing higher dispersion values than with gamma-rays. To compare the repair kinetics of both radiation qualities split-dose experiments were performed. A dose of 4 Gy gamma-rays (3 Gy neutrons) was delivered either as a single exposure or in two equal fractions separated by time intervals ranging from 30 min to 10 h (30 min to 7 h for neutrons). The data showed for gamma-rays a significant decline (30% +/- 10%) in MN yield with interfraction time due to repair of DNA damage. This repair is a continuous process starting almost immediately after the first of the two doses and lasting 3-5 h. For fast neutrons no decline was observed indicating irreparable damage.
1. The statistical nature of transmitter release was studied in unparalysed cut rat diaphragm using a voltage clamp technique at room temperature (23 degrees C). 2. While the binomial distribution described observed amplitude histograms well, the Poisson distribution was clearly inadequate. Values of m ranged from 40 to 45, while values for n varied from 45 to 53 and p was between 0.82 and 0.90. 3. Estimation of the probability of release from the transient decay of e.p.c.s in short tetanic trains (11 pulses, 150 Hz) gave values of p from 0.031 to 0.054, which are more than one order of magnitude lower than statistical estimates. 4. As a result of the short tetanic stimulation (5 pulses, 20, 50 and 100 Hz) there is an initial transient facilitation which afterwards becomes masked by depression. Statistical analysis suggests that the changes in the average numbers of quanta released (m) could be attributed to the change in the immediately available store (n). 5. During long tetanic stimulation (4000 pulses, 10-100 Hz) statistical analysis suggests that the decrease in the average number of quanta released (m) could be attributed almost entirely to the decrease in the immediately available store (n). The probability of release (p) decreased only slightly. The extent of the post-tetanic potentiation indicates that it cannot be explained on the grounds of increased probability of release (p) only. There should be an increase as well in the immediately available store (n). 6. It is suggested that while depression is most likely caused by the depletion of the immediately available store due to insufficient replenishment, the facilitation is probably caused by the increase in the capacity of the immediately available store to contain transmitter.
It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account.
BACKGROUND: Previous attempts to decide whether there is significant year-to-year variation in the birth rate of people who subsequently develop schizophrenia have given conflicting results, probably because of differences in the statistical methods employed. AIMS: To determine whether there is significant year-to-year variation in the birth rate. METHOD: Variation in the birth rate for the period 1921-1960 was studied in three separate national data sets--English, Danish and Scottish--using cubic splines to smooth the distribution curve before calculating residuals from a Poisson distribution. RESULTS: Over-dispersion was found in all three data sets, particularly in the Danish and Scottish data. However, the correlation between the sets of standardised residuals derived from the three data sets was only statistically significant for Denmark v. England. CONCLUSIONS: There was statistically significant year-to-year variation in the birth rate of people who subsequently developed schizophrenia in three countries in north-west Europe in the years 1921-1960. This is potentially a clue to the nature of the environmental determinants of schizophrenia, but better data will be needed before useful explanatory hypotheses can be generated and tested.
When mitoses are randomly distributed in a given area, the distribution of the mitotic density follows a Poisson distribution and the variance V equals the mean M. When mitotic synchronization exists the variance becomes greater than the mean. It is shown that, if p is the probability of mitotic synchronization between "sister" cells, the ratio V/M = (1 + 3p)/(1 + p).