Barbara Heller

Statistics of enumerating total coliforms in water samples by membrane filter procedures

Abstract A commonly used assumption is that the microbial counts of a given water sample are randomly distributed according to Poisson statistics and, in particular, that replicate analyses of the same sample are so distributed. Using Fishers index of dispersion, as well as a newly developed test, analysis of prior data on membrane filter total coliform organisms in a variety of water samples indicated that, in many cases, the assumption of Poisson statistics was incorrect, but that the data were consistent with a negative binomial distribution. This finding has significance in the interpretation of total coliform counts for regulatory as well as research purposes, and further research to delineate the responsible mechanisms is required.

Acute and persistent effects of methamphetamine on developing monoaminergic neurons in reaggregate tissue culture

Three-dimensional, rotation-mediated reaggregate tissue cultures composed of rostral mesencephalic cells and corpus striatal cells were used to examine the short-term and persistent effects of methamphetamine on developing monoamine-containing neurons. Reaggregates were exposed to drug for one week. Reductions in reaggregate endogenous dopamine and serotonin levels occurred following treatment with methamphetamine during days 15-22 of culture over the concentration range 10(-7) to 10(-4) M. The highest methamphetamine concentration reduced dopamine and serotonin levels to 29 and 33%, respectively, of control values. Monoamine levels were reduced from control values after 3 days of exposure to 10(-4) M methamphetamine. No further reduction resulted from 4 additional days of drug treatment. In order to determine whether monoaminergic neurons would recover from the drug-induced deficit, reaggregates were exposed to 10(-4) M methamphetamine for 7 days and then grown in drug-free media for an additional 20 days. During the 20 day recovery period, monoamine levels in the control group increased with time in culture. After an initial rapid increase (recovery days 0-9), the level of monoamines in the recovery group remained at a constant proportion to the level in the control group suggesting that the monoaminergic neurons return to a rate of development similar to that seen in untreated cultures. However, this rate was not sufficient to overcome the reduction in monoamine levels produced by 7 days of methamphetamine treatment. The results indicate that the effects of methamphetamine on developing monoaminergic neurons are marked and persistent.

Coherent states and Bayesian duality

We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions. It turns out that nonlinear coherent states, of the type widely studied in quantum optics, are a particularly useful class of coherent states from this point of view, in that they contain many of the standard statistical distributions. We also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions.

Kinetics of inactivation of Giardia lamblia by free chlorine.

Abstract The experimental data of Hibler on the inactivation of Giardia cysts by free chlorine was analyzed by the method of maximum likelihood. It was found that the Hom model with an m value less than 1 (indicative of “tailing off”) more precisely characterized the inactivation than the Chick-Watson model. The Hom model was found to fit the data using a Monte Carlo procedure to obtain the sampling distribution of the log likelihood statistic. The jackknife procedure was used to produce interval estimates for inactivation rate parameters and et values at various concentrations, temperatures, pH values and degrees of inactivation. The et values increase as concentration increases due to coefficients of dilution less than one. The computed et values are generally lower, and, particularly at 2–3 logs inactivation substantially lower, than those previously estimated from the same data by Hibler and by Clark et al. The difference is attributed to the manner in which these workers lumped results in which from 1 to 4 (of 5) animals were infected and interpreted them as arising from 4 logs inactivation. At both 2.5 and 5°C, there is a consistent increase in the required et value with pH. However at 0.5°C, the et values at pH 8 are less than those required at pH 7, contrary to anticipated. At pH 6, there is a consistent decrease in required et values as temperature increases. However at pH 7 and pH 8, the effect of temperature is more irregular. Due to the apparent anomalies in the pH and temperature dependence of the et values no procedure for extrapolation of the inactivation results outside the range of conditions used by Hibler can be recommended.

In vitro evidence that the reduction in mesencepalic dopaminergic neurons in the weaver heterozygote is not due to a failure in target cell interaction

Abstract The murine weaver (wv) mutation is characterized by a genetically determined loss of several neuronal populations, which include the nigrostriatal dopaminergic neurons. Animals homozygous for the wv gene exhibit marked deficits in dopaminergic morphological and neurochemical parameters. The wv gene shows incomplete dominance in that heterozygous (wv/+) mice exhibit moderate reductions in midbrain dopaminergic neuron number. It is unclear whether the dopaminergic neuronal loss in homozygous and heterozygous animals results from an effect of the wv gene solely on the dopaminergic neurons or is due to a failure of interaction of dopaminergic neurons with target cells of the striatum. This issue has been addressed utilizing three-dimensional reaggregate tissue cultures to determine whether the wv gene acts directly on the mesencephalic dopaminergic neurons. Embryonic mesencephalon and striatum from wv/+ and wild-type (+/+) brains were dissociated and the cells recombined into four mesencephalic-striatal aggregate combinations: (1) mesencephalic(+/+)-striatal(+/+)aggregates; (2) mesencephalic(wv/+)-striatal(wv/+)aggregates; (3) mesencephalic(wv/+)-striatal(+/+)aggregates; and (4) mesencephalic(+/+)-striatal(wv/+)aggregates. At 29 days and 57 days of culture, the number of dopaminergic neurons and dopamine content from mesencephalic-striatal aggregates consisting of mixed genotype or from only wv/+ tissue were quantitated and compared with that from mesencephalic-striatal cultures prepared from +/+ tissue alone. At both culture time points, aggregates containing wv/+ mesencephalon coaggregated with either wv/+ or +/+ striatum contained fewer dopaminergic neurons than mesencephalic-striatal cultures composed of only +/+ cells. Coaggregation of +/+ mesencephalon with wv/+ striatum did not have a detrimental effect on dopaminergic cell number. The findings demonstrate that the difference in the number of mesencephalic dopaminergic neurons between wv/+ and +/+ animals seen in vivo can be reproduced in three-dimensional reaggregate culture. Since the coculture of +/+ striatum with wv/+ mesencephalon did not appear to rescue wv/+ dopaminergic neurons in the aggregates as compared to wv/+ striatum and, wv/+ striatum proved to be a perfectly adequate target for +/+ mesencephalic dopaminergic neurons, it appears that the effect of the wv gene is on the dopaminergic neurons themselves.

Group invariant inferred distributions via noncommutative probability

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the latter method. We consider the Poisson and binomial distributions in detail to illustrate a groupinvariance method to obtain inferred distributions on the parameter spaces conditional upon observed results. The families are constructed according to group theoretic methods involving so-called coherent states . These particular inferred distributions coincide with Bayesian posteriors. In that sense, this context provides a method for obtaining noninformative prior measures. The proposed method yields uniform priors on the canonical parameters for both the Poisson and binomial distributions.

Computer experiments to determine whether over- or under-counting necessarily affects the determination of difference in cell number between experimental groups.

Computer cell counting experiments were performed in order to examine the consequences of over- or under-counting. The three-dimensional reaggregate culture laboratory environment for cell counting was used as a model for computer simulation. The laboratory environment for aggregate and cell sizes, numbers and spatial placement in gelatin blocks was mimicked in the computer setup. However, in the computer, cell counting was set to be either ideally unbiased, or deliberately biased in regard to over- or under-counting so as to compare eventual results when using the various cell counting methods. It was found that there was no effect of the cell counting methods used in determining whether there was a significant difference in cell number between two experimental groups. In addition, it was found that under the conditions of these simulations, the optical dissector method behaved similarly, on the average, as the ideal method of counting cell centers and in both of those cases, the average ratio between actual cell number in a flask and estimated number was close to 1.00.

Positive-Operator Valued Measure (POVM) Quantization

Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;E-Mail: heller@iit.edu* Authors to whom correspondence should be addressed; E-Mail: gazeau@apc.univ-paris7.fr;Tel.: +331-5727-6049; Fax: +331-5727-6071.Academic Editor: James D. MalleyReceived: 3 September 2014 / Accepted: 18 December 2014 / Published: 25 December 2014Abstract: We present a general formalism for giving a measure space paired with a separableHilbert space a quantum version based on a normalized positive operator-valued measure.The latter are built from families of density operators labeled by points of the measurespace. We especially focus on various probabilistic aspects of these constructions. Simple ormore elaborate examples illustrate the procedure: circle, two-sphere, plane and half-plane.Links with Positive-Operator Valued Measure (POVM) quantum measurement and quantumstatistical inference are sketched.Keywords: POVM; quantization; covariance; density operators; quantum measurement1. IntroductionIn this paper, we propose a quantum analysis, generally non-commutative, of a measurespace based on a (normalized) positive-operator valued measure ((N)POVM) (in order not tospoil the text with too many acronyms, we will keep “POVM” in our paper to designate anormalized positive operator-valued measure) built from a density matrix or operator (in thequantum mechanics terminology) acting on some separable Hilbert space. One key aspect of

Quantitation of dopaminergic neurons in 3-dimensional reaggregate tissue culture by computer-assisted image analysis

Three-dimensional (3D) reaggregate tissue culture provides a means of quantitatively assessing neuronal cell survival under a variety of experimental conditions. A method is presented for estimation of, and comparison between, the total numbers of cells of a given neurochemical type within individual experimental flasks. The method involves cell counting from random reaggregate sections, determination of sectional volumes, and of 3D reaggregate volumes by a novel image-analysis computer system.

Special functions and characterizations of probability distributions by zero regression properties

Characterizations of the binomial, negative binomial, gamma, Poisson, and normal distributions are obtained by the property of zero regression of certain polynomial statistics of arbitrary degree, on the mean. In each case, the equations which express zero regression are derived from the recurrence relations of a set of special functions. The differential recurrence relations of these special functions are used in the proofs of the characterization theorems.