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On the prediction of simultaneous inbreeding coefficients at multiple loci.

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Data Interpretation, Statistical↗

The reproducibility of forced expiratory wheezes.

Previous work has shown forced expiratory wheezes (FEW) to be associated with onset of flow limitation and to have spectral characteristics similar to wheezes heard in patients with obstructive lung diseases. This study was designed to determine whether the acoustic characteristics of FEW are reproducible under controlled lung volume and flow conditions. Six healthy, nonsmoking young adults 28 to 37 yr of age were studied. They performed FVC maneuvers through a set of round apertures (diameters, 14, 12, 10, 8, 6, 4, 2, and 1 mm). Flow, measured with a pneumotachograph, and tracheal lung sounds, recorded with a Hewlett-Packard HP20510A contact sensor, were recorded simultaneously on magnetic tape and analyzed off-line. For each subject, data from three different aperture sizes, measured in triplicates, were analyzed (total of 54 runs); 199 different wheezes were identified (mean, 3.7 wheezes/run), and 56.7 +/- 5.1% (mean +/- SEM) of wheezes found in a certain run (range, 41.7 to 77.8%) were identical to wheezes found in the other two runs of the same aperture size (i.e., same flow rate). In 17 of the 18 sets of triplicate runs analyzed, at least one major wheeze was identical in all three runs of the set. In three of the sets, two different identical wheezes were found. These findings support a deterministic mechanism of generation of wheezes and is in line with the predictions of the "flutter theory."

Adult↗

Beyond Rayleigh's criterion: a resolution measure with application to single-molecule microscopy.

Rayleigh's criterion is extensively used in optical microscopy for determining the resolution of microscopes. This criterion imposes a resolution limit that has long been held as an impediment for studying nanoscale biological phenomenon through an optical microscope. However, it is well known that Rayleigh's criterion is based on intuitive notions. For example, Rayleigh's criterion is formulated in a deterministic setting that neglects the photon statistics of the acquired data. Hence it does not take into account the number of detected photons, which, in turn, raises concern over the use of Rayleigh's criterion in photon-counting techniques such as single-molecule microscopy. Here, we re-examine the resolution problem by adopting a stochastic framework and present a resolution measure that overcomes the limitations of Rayleigh's criterion. This resolution measure predicts that the resolution of optical microscopes is not limited and that it can be improved by increasing the number of detected photons. Experimental verification of the resolution measure is carried out by imaging single-molecule pairs with different distances of separation. The resolution measure provides a quantitative tool for designing and evaluating single-molecule experiments that probe biomolecular interactions.

Calibration↗

Transmissibility of 1918 pandemic influenza.

The 1918 influenza pandemic killed 20-40 million people worldwide, and is seen as a worst-case scenario for pandemic planning. Like other pandemic influenza strains, the 1918 A/H1N1 strain spread extremely rapidly. A measure of transmissibility and of the stringency of control measures required to stop an epidemic is the reproductive number, which is the number of secondary cases produced by each primary case. Here we obtained an estimate of the reproductive number for 1918 influenza by fitting a deterministic SEIR (susceptible-exposed-infectious-recovered) model to pneumonia and influenza death epidemic curves from 45 US cities: the median value is less than three. The estimated proportion of the population with A/H1N1 immunity before September 1918 implies a median basic reproductive number of less than four. These results strongly suggest that the reproductive number for 1918 pandemic influenza is not large relative to many other infectious diseases. In theory, a similar novel influenza subtype could be controlled. But because influenza is frequently transmitted before a specific diagnosis is possible and there is a dearth of global antiviral and vaccine stores, aggressive transmission reducing measures will probably be required.

Cities↗

Cell orientation induced by extracellular signals.

Cells like fibroblasts and osteoblasts are oriented by different extracellular guiding signals like an electric field, a bent surface, and a periodically stretched surface. An automatic controller is responsible for the cell alignment. The controller contains both a deterministic and a stochastic signal. The following machine properties were determined: (1) The angle dependence of the cellular signal transformer is cos 2(psi 0 - psi). (2) The set point of the automatic controller is psi 0 = +/- 90 degrees. The cells like to orient their long axis perpendicular to the direction of the applied guiding signal. (3) The signal transformer measures the extracellular signal in a quadratic fashion. The cells cannot register the sign of the guiding field. (4) The stochastic signal in the automatic controller can be quantified by a characteristic time (approximately 130 min for fibroblasts). (5) The extracellular signal is registered in cell-made standards (ratio of the deterministic and stochastic signal equals one): 0.3 +/- 0.05 V/mm for human fibroblasts (electric field) and 85 +/- 3 microns for human fibroblasts and osteoblasts (cyclindrically bent surface). (6) The lag-time in the signal transduction system of fibroblasts is approximately 4 min.

Cell Polarity↗

On the comparative static properties of the expected population density in the presence of stochastic fluctuations.

We consider the impact of increased stochastic fluctuations on the expected density of an unstructured population evolving according to a regular diffusion process subject to a concave expected growth rate. By relying on the flow nature of the solutions of stochastic differential equations and Girsanov's theorem, we demonstrate that typically increased volatility decreases the expected future population density. As a consequence, we are able to characterize the sensitivity of the expected population density with respect to changes in the diffusion coefficient measuring the size of the stochastic fluctuations. We provide both qualitative and quantitative information about the consequences of a mis-specified volatility structure and, especially, of a deterministic approximation to stochastic population growth. We also consider the effect of uncertainty in the initial density and demonstrate that the sign of the relationship between the expected population density and initial uncertainty is unambiguosly negative.

Animals↗

Oscillatory, stochastic and chaotic growth rate fluctuations in permittistatically controlled yeast cultures.

We describe a continuous culture system related to the turbidostat, but using a feedback system based on biomass estimation from the dielectric permittivity of the cell suspension rather than its optical density. It is shown that this system provides an excellent method of maintaining a constant biomass level within a fermentor. The computer-controlled system was able to effect the essentially continuous registration of growth rate by monitoring the rate of medium addition via the time-dependent activity of the pump. At some biomass setpoints for aerobically grown cultures of baker's yeast substantial time-dependent fluctuations in the growth rate of the culture were thereby observed. At some biomass setpoints, however, or under anaerobic conditions, or when using a non-Crabtree yeast, the growth rate was constant, indicating that the fluctuations were inherent to the biological system and not simply a property of the fermentor and control system. A variety of time series analyses (Fourier transformations, Hurst and Lyapunov exponents, the determination of embedding dimension, and non-linear time series predictions based on the methodology of Sugihara and May) were used to demonstrate, for the first time, that as well as stochastic and periodic components these fluctuations exhibited deterministic chaos. 'Trivial predictors' were unable to give accurate predictions of the growth rate in these cultures. The growth rate fluctuations were studied further by means of offline measurements of changes in percentage viability, bud count, and in the external ethanol and glucose concentrations; these data and other evidence suggested that the growth rate fluctuations were closely linked to the primary respiro-fermentative metabolism of this organism. The identification of chaotic growth rates in cell cultures suggests that there may be novel methods for controlling the growth of such cultures.

Biomass↗

Quantitative estimation of uncertainty in human risk analysis.

This paper is aimed to candidate the use of an ISO standard procedure (Guide to the Expression of Uncertainty in Measurement, GUM) for quantitative evaluation of uncertainty in Human Risk estimation under chronic exposure to a hazardous chemical compound. Risk was evaluated by using the usual methodologies: the deterministic reasonable maximum exposure (RME) and the statistical Monte Carlo method; in both cases the procedures to evaluate the uncertainty on risk values are detailed. The paper put in evidence that the procedure is able to single out the variables that contribute mostly to the uncertainty. The obtained results show that the application of GUM procedure is easy and straightforward to estimate the uncertainty value on the results of risk estimation. The procedure is applied to a real case concerning the ingestion of milk contaminated by dioxins in a northern part of Italy; the risk value resulted to be over the minimal threshold of 10(-6) with 20-80% confidence.

Animals↗

Application of a population balance model to a perfusion in vitro toxicity system.

Perfusion cell culture is different to static cell culture: In perfusion culture, steady state concentrations of nutrients and metabolites can be achieved. When a toxin is added to the medium, it is administered to the cells at a defined constant concentration. Perfusion culture is favourable for time series analysis of experimental data because assays can be performed online in the outflowing medium at a high time resolution. The cytotoxicity exerted by cadmium chloride (CdCl(2)) on LLC-PK(1) cells was investigated in static and in perfusion culture using the EpiFlow system in order to compare both the techniques. For this comparison, cytotoxicity was assessed by the release of the cytosolic enzyme lactate dehydrogenase (LDH), and by the potential of viable cells to reduce resazurin. The results showed a greater sensitivity of LLC-PK(1) monolayers to CdCl(2) with continuous exposure in perfusion culture as compared to a single or repeated dose in static culture, as evidenced by increased LDH release and decreased resazurin reduction. These differences between static and perfusion culture were ascribed to different delivery rates of toxin to the site of absorption. Cadmium accumulation of the cells was measured and found to be higher under perfusion conditions than under static conditions. Time series analysis of the LDH release in perfusion culture was performed by establishing a deterministic population balance model of cell death. An empirical death rate function that accounts for accumulation of the toxin was introduced and could be successfully verified.

Algorithms↗

Infectious disease persistence when transmission varies seasonally.

The generation reproduction number, R0, is the fundamental parameter of population biology. Communicable disease epidemiology has adopted R0 as the threshold parameter, called the basic case reproduction number (or ratio). In deterministic models, R0 must be greater than 1 for a pathogen to persist in its host population. Some standard methods of estimating R0 for an endemic disease require measures of incidence, and the theory underpinning these estimators assumes that incidence is constant through time. When transmission varies periodically (e.g., seasonally), as it does for most pathogens, it should be possible to express the criterion for long-term persistence in terms of some average transmission (and hence incidence) rate. A priori, there are reasons to believe that either the arithmetic mean or the geometric mean transmission rate may be correct. By considering the problem in terms of the real-time growth rate of the population, we are able to demonstrate formally that, to a very good approximation, the arithmetic mean transmission rate gives the correct answer for a general class of infection functions. The geometric mean applies only to a highly restricted set of cases. The appropriate threshold parameter can be calculated from the average transmission rate, and we discuss ways of doing so in the context of an endemic vector-borne disease, canine leishmaniasis.

Animals↗

Assessing clinically relevant perceptual organization with multidimensional scaling techniques.

Multidimensional scaling (MDS) techniques provide a promising measurement strategy for characterizing individual differences in cognitive processing, which many clinical theories associate with the development, maintenance, and treatment of psychopathology. The authors describe the use of deterministic and probabilistic MDS techniques for investigating numerous aspects of perceptual organization, such as dimensional attention, perceptual correlation, within-attribute organization, and perceptual variability. Additionally, they discuss how formal quantitative models can be used, in conjunction with MDS-derived representations of individual differences in perceptual organization, to test theories about the role of cognitive processing in clinically relevant phenomena. They include applied examples from their work in the areas of eating disorders and sexual coercion.

Coercion↗

Detecting and characterizing phase synchronization in nonstationary dynamical systems.

We propose a general framework for detecting and characterizing phase synchronization from noisy, nonstationary time series. For detection, we propose to use the average phase-synchronization time and show that it is extremely sensitive to parameter changes near the onset of phase synchronization. To characterize the degree of temporal phase synchronization, we suggest to monitor the evolution of phase diffusion from a moving time window and argue that this measure is practically useful as it can be enhanced by increasing the size of the window. While desynchronization events can be caused by either a lack of sufficient deterministic coupling or noise, we demonstrate that the time scales associated with the two mechanisms are quite different. In particular, noise-induced desynchronization events tend to occur on much shorter time scales. This allows for the effect of noise on phase synchronization to be corrected in a practically doable manner. We perform a control study to substantiate these findings by constructing and investigating a prototype model of nonstationary dynamical system that consists of coupled chaotic oscillators with time-varying coupling parameter.

Algorithms↗

Optical realization of optimal unambiguous discrimination for pure and mixed quantum states.

Quantum mechanics forbids deterministic discrimination among nonorthogonal states. Nonetheless, the capability to distinguish nonorthogonal states unambiguously is an important primitive in quantum information processing. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three nonorthogonal states, with a success rate of 55%, to be compared with the 25% maximum achievable using projective measurements. Furthermore, we present the first realization of unambiguous discrimination between a pure state and a nonorthogonal mixed state.

Journal Article↗

Time-series analysis. Use of autocorrelation as an analytic strategy for describing pattern and change.

Although graphic representation of time-series data is one method to describe patterns of phenomena, autocorrelations, correlograms, and plots of the autocorrelation function provide descriptive and statistical methods that reveal the structure of a deterministic cycle component within the time-series. The autocorrelation function provides a method for the investigator to test hypotheses about the nature and pattern of relationships between measured and latent variables. Patterns of phenomena can be analyzed statistically using objectively provided criteria. The autocorrelation function can also be used to understand the change in response or behavioral patterns following an experimental intervention. Traditional group comparison designs, using cross-sectional data collection strategies cannot identify differences within the individual nor can they identify patterns of behavior or structural patterns within the data. Autocorrelation and cross-correlation become threats to statistical validity when conventional methods are used; however, in time-series analysis, autocorrelation allows close scrutiny of the pattern of response within an individual across a time-dimension.

Data Interpretation, Statistical↗

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).

Animals↗

The California Automated Mortality Linkage System (CAMLIS).

The California Automated Mortality Linkage System (CAMLIS), established in 1981 to facilitate the conduct of follow-up studies in the State of California, employs a combination of deterministic and probabilistic linkage decision criteria to perform the death clearance function. The system was evaluated against four traditional death clearance procedures and the performance of each procedure measured in terms of measures of sensitivity and specificity. Only one procedure was associated with a specificity lower than 0.99; for that one, the specificity was 0.93. There was much greater fluctuation in the observed sensitivity levels. In one of the procedures, CAMLIS demonstrated a sensitivity of 0.97 versus 0.79 for the Social Security Administration. A comparison against the National Death Index (NDI) produced sensitivities of 0.89 for CAMLIS and 0.94 for the NDI. An assessment of manual search procedures using a file of Japanese names produced a CAMLIS sensitivity measure of 0.92 compared with 0.93 for the manual search. Another manual search procedure using microfiche copies of the state death index produced a CAMLIS sensitivity of 0.97; in this evaluation, the sensitivity of the manual search was defined as 1.0. Another measure of performance of a death clearance procedure is its predictive value in identifying a person who has died; CAMLIS generated predictive values in these evaluations that ranged from 0.93 through 0.99, contrasted with the NDI value of 0.59.

California↗

Great Lakes monitoring results--comparison of probability based and deterministic sampling grids.

The Great Lakes may be viewed as a coastal environment, affected by the same meteorological and physical forces as the coastal ocean. The U.S. EPA, Great Lakes National Program Office (GLNPO) has monitored the open waters of the lakes, annually, since 1983. As part of the U.S. EPA Environmental Monitoring and Assessment Program (EMAP), a pilot study was performed in Lake Michigan to compare the existing GLNPO deterministic sampling grid with the EMAP probabilistic grid. Results of chemical analyses of trophic status indicators (total phosphorus and chlorophyll a) as well as nutrients and conventional limnological measurements, from spring and summer surveys in 1992 indicate little difference between the grids in the offshore region of the lake. The few statistically significant differences may be due to station distribution throughout the lake, or simple chance. This might be expected due to the well mixed nature of the open waters of Lake Michigan. The detection of a long-term trend for total phosphorus in Lake Michigan benefits from an annual program: viewing cumulative frequency distributions based on a four year EMAP interval does not convey information on the decrease in phosphorus in the lake. If the EMAP sampling grid were to be used in the Great Lakes, pilots in each of the lakes would be necessary for utilization of the existing long-term record as a basis for trend detection.

Data Collection↗

Test of synergistic interactions among deleterious mutations in bacteria.

Identifying the forces responsible for the origin and maintenance of sexuality remains one of the greatest unsolved problems in biology. The mutational deterministic hypothesis postulates that sex is an adaptation that allows deleterious mutations to be purged from the genome; it requires synergistic interactions, which means that two mutations would be more harmful together than expected from their separate effects. We generated 225 genotypes of Escherichia coli carrying one, two or three successive mutations and measured their fitness relative to an unmutated competitor. The relationship between mutation number and average fitness is nearly log-linear. We also constructed 27 recombinant genotypes having pairs of mutations whose separate and combined effects on fitness were determined. Several pairs exhibit significant interactions for fitness, but they are antagonistic as often as they are synergistic. These results do not support the mutational deterministic hypothesis for the evolution of sex.

Directed Molecular Evolution↗