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PubMed2000

Learning overcomplete representations.

In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can be sparser, and can have greater flexibility in matching structure in the data. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Previous work has focused on finding the best representation of a signal using a fixed overcomplete basis (or dictionary). We present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data. We show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency. This can be viewed as a generalization of the technique of independent component analysis and provides a method for Bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures.

Algorithms↗

PubMed2002

Quantitative study of breast cancer progression: different pathways for various in situ cancers.

The chromatin pattern in nuclei from breast ductal proliferative lesions was quantitatively evaluated with the objective of deriving measures of tumor progression. A total of 110 cases were analyzed. There were 38 cases of normal tissue or benign proliferative lesions, 41 cases of ductal carcinoma in situ (DCIS), and 31 cases of microinfiltrating DCIS and of infiltrating cancer. A total of 9424 nuclei were analyzed. High-resolution images were digitally recorded. For each nucleus, 93 karyometric features descriptive of the spatial and statistical distribution of the nuclear chromatin were computed. Data analysis included establishing a profile of relative deviations of each feature from "normal," called the nuclear signature, and of lesion signatures as well as of trends of lesion progression. Two trends of evolution could be discerned: one from normal to hyperplasia, atypical hyperplasia, and comedo DCIS as representative of high-grade lesions; and the other from normal to hyperplasia to cribriform DCIS, solid DCIS, and infiltrating cancer, representing lower grade lesions. The nuclei in microinfiltrating foci are distinctly different from nuclei in high-grade comedo DCIS. The nuclei in microinfiltrating foci have a statistically significantly lower nuclear abnormality. They may represent outgrowing clones.

Breast↗

PubMed1996

Using neural networks to model conditional multivariate densities.

Neural network outputs are interpreted as parameters of statistical distributions. This allows us to fit conditional distributions in which the parameters depend on the inputs to the network. We exploit this in modeling multivariate data, including the univariate case, in which there may be input-dependent (e.g., time-dependent) correlations between output components. This provides a novel way of modeling conditional correlation that extends existing techniques for determining input-dependent (local) error bars.

Economics↗

PubMed1991

Correlations between directional and orientational tuning of cells in cat striate cortex.

Simple (N = 284) and complex cells (N = 125) in the central projection area (0-5 degrees eccentricity) of the striate cortex of cats were stimulated with moving light bars and the responses to different directions of movement were recorded and plotted as polar-plots. Fourier analysis was applied to polar plots (SDO-analysis, Wörgötter and Eysel 1987; Wörgötter et al. 1990) to determine the general sensitivity (S) of the cells to visual stimulation, the directional (D) and orientational (O) tuning strength as well as preferred direction (PD) and preferred orientation (PO). Statistical distributions of the S, D and O parameters were determined for simple and complex cells of the cortical layers II-VI. Simple cells were more strongly tuned for direction and orientation than complex cells, whereas complex cells had a greater general sensitivity to visual stimulation. Directional tuning was significantly stronger in layer VI than in layer IV simple cells, otherwise no differences were detected between these two layers. We found that cells with large D and small O components are generally rare. The D and O components were plotted against each other to determine any possible correlation between the tuning strengths. The correlations were statistically significant for simple and complex cells but the correlation coefficients were very small (r less than 0.3). It is suggested that only a very weak coupling between directional and orientational tuning exists, preferentially in the deeper layer simple cells.

Animals↗

PubMed2001

Numerical analysis of a model of organ motion using serial imaging measurements from prostate radiotherapy.

We previously proposed a model for incorporating the effects of organ motion, including the changes in organ shape, into the calculation of dose in a statistical fashion based on serial imaging measurements of organ motion. In the present paper, numerical studies were used to investigate how the accuracy of the statistical calculation of dose depends on the number of organ motion measurements provided as input into the model. The dose calculated statistically with the model was consistently more accurate than the one obtained by directly resampling the serial measurements of organ motion. It was also more robust relative to the random variabilities present in the input organ motion measurements. The results confirm that the model can reproduce the statistical distribution of the organ motions measured in a serial imaging study, including the changes in organ shape, without making any assumptions about the functional form of this distribution. The model allows a more accurate calculation of dose to be performed from a given number of measurements of organ motion than would otherwise be obtained by directly resampling the measured data. It thus maximizes the information that is extracted from serial imaging measurements.

Algorithms↗

PubMed1986

A mathematical model of survival kinetics. I. Theoretical basis.

A mathematical model of mortality and survival kinetics is proposed based upon the two main aspects of survival data, namely, the rate of vitality reduction with age and its statistical distribution. Certain mathematical assumptions are made on the time-course of both vitality and its distribution. Then, these two aspects are integrated in a single model which can be used to describe survivorship, cumulative mortality or dying. The model is capable of fitting empirical curves even at very advanced ages, where the widely used Gompertz law fails. Examples are provided, derived from populations having rather different lifespans such as rotifers, flies, rats and horses. The model maintains one of the most interesting characteristics of Gompertz law, namely, the possibility to estimate the 'design constant for longevity' relating maximum lifespan to one of the parameters of the model. It also has the potential characteristics enabling it to be used to judge the statistical significance of the difference between two empirical survival curves.

Aging↗

PubMed2003

Conformational flexibility of the group B meningococcal polysaccharide in solution.

To elucidate the role of secondary structure in the immune response against alpha(2-->8)-linked polysialic acid, the capsular polysaccharide of Group B meningococci, we have investigated its solution dynamics by using specific models of molecular motion and hydrodynamic modeling to interpret experimental NMR data. (13)C-[(1)H] NMR relaxation times and steady-state NOE enhancements were measured for two aqueous solutions of alpha(2-->8)-linked sialic acid polysaccharides. Each contained a unique distribution of polysaccharide chain lengths, with average lengths estimated at 40 or 400 residues. Models for rigid molecule tumbling, including two based on helical conformations proposed for the polysaccharide,(31) could not explain the NMR measurements. In general for these helices, the correlation times for their overall tumbling that best account for the NMR data correspond to polysaccharide chains between 9 and 18 residues in length, far short of the average lengths estimated for either solution. The effects of internal motions incorporated into these helices was modeled with an effective correlation time representing helix tumbling as well as internal motion. This modeling demonstrated that even with extreme amounts of internal motion, "flexible helices" of 25 residues or more still could not produce the NMR measurements. All data are consistent with internal and segmental motions dominating the nuclear magnetic relaxation of the polysaccharide and not molecular tumbling. Statistical distributions of correlation times have been found specifically for the pyranose rings, linkage groups, and methoxy groups that can account for the measured relaxation times and NOE enhancements. The distributions suggest that considerable flexibility attends the polysaccharide in solution, and the ranges of motional frequencies for the linkage groups and pyranose rings are comparable. We conclude that the Group B meningococcal polysaccharide is a random coil chain in solution, and therefore, does not have antigenic epitopes dependent upon a rigid, ordered conformation.

Bacterial Capsules↗

PubMed1984

Simultaneous determination of trace elements in serum by energy-dispersive x-ray fluorescence spectrometry.

Energy-dispersive x-ray fluorescence is applied in the analysis of human serum to determine the concentrations of several elements simultaneously with minimal manipulation of the sample. The analytical procedure has been developed with standard sera, and standardization, detection limits, and reproducibility have been established. A 50-microL sample of diluted serum, to which an internal standard has been added, is deposited on a thin (4-microns thick) polypropylene film and analyzed by x-ray fluorescence. We report the statistical distributions of the concentrations of Fe, Cu, Zn, and Br obtained in the population (103 samples) studied, and report detection limits for the other 22 elements studied. The simplicity of the method, the high throughput, and the possibility of automating the measurements make this procedure suitable for screening large numbers of sera.

Bromine↗

PubMed1975

[Hereditary melanotic tumors of Drosophila. Determination of the tumorous transformation of larva hemocytes].

Two different phenomena contribute to the histogenesis of melanotic formations in tumoral strains of drosophila : an abnormal multiplication of certain blood cells and their encapsulation by normal hemocytes. The statistical distribution of melanotic tumors in populations of individuals submitted during precise periods of their life to the action of agents such as supraoptimal temperature or ionizing radiations, permits to suggest for the tumoral transformation of larval hemocytes in drosophila, the following mechanism : this transformation is caused by an event occuring in the cytoplasm and determined by the activity of a nuclear gene.

Animals↗

PubMed2003

Rank order metrics for quantifying the association of sequence features with gene regulation.

MOTIVATION: Genome sequences and transcriptome analyses allow the correlation between gene regulation and DNA sequence features to be studied at the whole-genome level. To quantify these correlations, metrics are needed that can be applied to any sequence feature, regardless of its statistical distribution. It is also desirable for the metric values to be determined objectively, that is, without the use of subjective threshold values. RESULTS: We compare two metrics for quantifying the correlation of DNA sequence features with gene regulation. Each of the metrics is calculated from a rank-ordering of genes based on the value of the sequence feature of interest. The first metric is the area under the curve for a receiver operator characteristic plot (ROC AUC), a common way of summarizing the tradeoff between sensitivity and specificity for different values of a prediction criterion. We call the second metric the mean normalized conditional probability (MNCP). The MNCP can be thought of as the predictive value of the sequence feature averaged over all regulated genes. The statistical significance (P-value) of each metric can be estimated from simulations. Importantly, the P-value of the MNCP metric is less dramatically affected by the presence of false positives among the set of co-regulated genes than is the ROC AUC. This is especially useful in analyzing gene sets identified by DNA microarray analysis because such data cannot distinguish direct regulation by transcription factor binding from indirect regulation. We demonstrate that these two metrics, taken together, are useful tools for defining the binding site representation and regulatory control regions that best explain the difference between genes that are regulated by a given transcription factor and those that are not. Applications to other gene features are also described. AVAILABILITY: A Python program for calculating the ROC AUC and MNCP metric values given input rank orders is available from ftp://ftp.bs.jhmi.edu/users/nclarke/MNCP/

Algorithms↗

PubMed1998

Correlation of plasma clearance of 54 extensively metabolized drugs between humans and rats: mean allometric coefficient of 0.66.

PURPOSE: To evaluate the distribution of allometric exponents for relationship of total plasma clearance of 54 extensively metabolized drugs, with wide-ranging linear clearance values, between humans and rats, to provide a rationale for the observed data, and to discuss potential significance of the findings. METHODS: Human and rat plasma clearance values of 54 drugs with markedly different physicochemical properties were obtained from the literature. Standard allometric analysis was performed for each drug using both rat and human data. Unbound vs. total plasma clearances were obtained for 15 out of 54 drugs and their correlations between humans and rats were compared. RESULTS: The mean+/-SD of the allometric exponent for the 54 drugs studied is 0.660+/-0.190. The median clearance ratio based on unit body weight is 7.41 and the median exponent is 0.645. Excluding two outliers the correlation coefficient of plasma clearance between humans and rats was 0.745 (p < 0.0001). For the 15 drugs, use of unbound plasma clearance approach seems to significantly improve the correlation coefficient compared to total plasma clearance (0.940 vs. 0.841). CONCLUSIONS: The present study indicates that on average, humans and rats may eliminate extensively metabolized drugs at a rate similar to that expected from the allometric or body surface area relationship of basal metabolic rate between the two species. A simple statistical distribution hypothesis is used to rationalize the species difference in plasma drug clearance. Rat may serve as an useful animal model to predict (unbound) plasma clearance of drugs in humans.

Animals↗

PubMed1988

Distribution of embryos and 500-microM microspheres in the rabbit oviduct: controls for acute motion analysis during transport.

Distributions of embryos and 500-micron diameter microspheres were measured in the cleared oviducts of 32 rabbits at 8 intervals post coitus (pc) and normalized to percentage of isthmic length. By 18 h pc, 46% of the embryos had entered the isthmus and were denuded of the cumulus, while 55% of the microspheres had entered the isthmus. By 24 h pc, all embryos and microspheres were in the isthmus. At 72, 78, and 84 h pc, 6.5, 37, and 93% of embryos and 21, 73, and 95% of microspheres were in the cornu, respectively. The mean positions of embryos and microspheres progressed at approximately 1% of isthmic length per hour between 24 and 72 h pc. Throughout isthmic transport, embryos and microspheres in individual oviducts were tightly grouped and had similar statistical distributions. Although microspheres began to transfer into the uterine horns earlier than embryos, the data suggest that 500-micron microspheres can be used in studies to quantify discrete movements within the oviduct prior to 72 h pc. The data further suggest that opposing forces may be generated by contractile events that keep embryos grouped and possibly control their rate of progress through the oviduct.

Animals↗

PubMed1992

Stochastic population forecasts and their uses.

"The properties and uses of stochastic forecasts are discussed here. For linear stochastic projections, we show how the computation of forecast moments and the statistical distribution of forecasts depend on the multiplicative and autoregressive structure of the dynamics. Both scalar and vector projection methods are discussed, and their similarities are explored. Next we discuss the uses of stochastic forecasts, arguing that it is important to relate forecasts to the specific decision-making criteria of particular forecast users. The example of [the U.S. system of] Social Security is used to show how a dynamic programming approach may be used to explore alternative decisions in a probabilistic context."

Americas↗

PubMed1998

Understanding artificial neural networks and exploring their potential applications for the practicing urologist.

Artificial neural networks (ANNs) are complex mathematical models that are distantly based on the human neuronal structure. They are capable of modeling elaborate biologic systems without making assumptions based on statistical distributions. Preliminary work has been reported on their application in urology. The initial results have been promising, particularly as an additional tool in the detection of early prostate cancer using the ProstAsure Index, which has been the most extensively studied urologic ANN to date. We review the basic concepts behind ANNs and examine currently existing and potential future applications of this new dynamic technology both in urology and in general clinical medicine.

Clinical Medicine↗

PubMed1998

[Pressure-controlled mechanical ventilation: a simplified titration method of the extrinsic positive expiratory pressure].

OBJECTIVES: Extrinsic positive end-expiratory pressure (PEEPe) may improve gas distribution within the lungs, induce alveolar recruitment or, conversely, produce pulmonary overdistension, and modify the respiratory impedance. Under pressure-controlled mechanical ventilation (PCV) this phenomenon modifies the minute ventilation and the dynamic compliance of the respiratory system (Crs,dyn). This study was aimed to assess the incidence of a significant gain in Crs,dyn under the effect of PEEPe during PCV. STUDY DESIGN: Prospective, open, descriptive, case series study. PATIENTS: Surgical intensive care unit patients, under sedation, neuromuscular blockade and PCV because of severe hypoxaemia (ARDS or acute lung injury). METHODS: Four incremental levels of PEEPe (4 to 16 cmH2O) of 30 minute duration were applied. Crs,dyn, and PaO2/FIO2 were recorded at the end of each level of PEEPe. The resulting gain in Crs,dyn was calculated and considered as significant if it was greater than the upper limit of confidence (at 99.8%) of the statistical distribution of all the recorded gains. RESULTS: Thirty patients were included, median and extreme values (within brackets) of PaO2/FIO2 of 117 [53-230] and Crs,dyn without PEEPe of 29 [14.3-46.8] mL.cmH2O-1. Among the 120 recorded gains, a gain in Crs,dyn was found significant at least once in 15 tests of PEEPe out of 30. Within the two groups of patients, the increase in PaO2/FIO2 with incremental PEEPe was similar. The levels of PEEPe producing the greatest increase in Crs,dyn were not correlated with the increase in PaO2/FIO2. CONCLUSION: In 50% of the studied patients a significant gain in Crs,dyn was found, allowing a less traumatic PCV. These results suggest the clinical usefulness of this method of titration of PEEPe, which requires neither specific devices nor a disconnection of the patient.

Adult↗

PubMed1995

Adaptive control of drug dosage regimens using maximum a posteriori probability Bayesian fitting.

Optimal drug therapy can only be achieved if a drug is given in the right dosage regimen. Therefore the dosage regimen needs to be optimized, using the available information of the drug, the patient, and his disease. The optimization of drug therapy comprises two major steps: First, the clinician should define explicit therapeutic goals for each patient individually. Second, a strategy to achieve these goals with the greatest possible precision should be chosen. An overview of the optimization of drug therapy is presented, with special reference to maximum a posteriori probability (MAP) Bayesian fitting. Drug dosage optimization requires 1. measurement of a performance index related to the therapeutic goal, generally one or more plasma concentration measurements, 2. population pharmacokinetic parameters, including mean values, standard deviations, covariances and information on the statistical distribution, and 3. reliable software for adaptive control strategy and optimal dosage regimen calculation. The benefit of optimal drug therapy by adaptive control using MAP Bayesian fitting has been proven, resulting in improved patient outcome by improved efficacy of therapy and a reduction of adverse reactions, and in reduced costs, mainly due to a reduction of hospitalization. Newer strategies might replace the MAP Bayesian fitting procedure, if their advantage has been demonstrated convincingly, and if reliable and user-friendly software is available.

Bayes Theorem↗

PubMed1992

DNA damage caused by ionizing radiation.

A survey is given of continuous-time Markov chain models for ionizing radiation damage to the genome of mammalian cells. In such models, immediate damage induced by the radiation is regarded as a batch-Poisson arrival process of DNA double-strand breaks (DSBs). Enzymatic modification of the immediate damage is modeled as a Markov process similar to those described by the master equation of stochastic chemical kinetics. An illustrative example is the restitution/complete-exchange model. The model postulates that, after being induced by radiation, DSBs subsequently either undergo enzymatically mediated restitution (repair) or participate pairwise in chromosome exchanges. Some of the exchanges make irremediable lesions such as dicentric chromosome aberrations. One may have rapid irradiation followed by enzymatic DSB processing or have prolonged irradiation with both DSB arrival and enzymatic DSB processing continuing throughout the irradiation period. Methods for analyzing the Markov chains include using an approximate model for expected values, the discrete-time Markov chain embedded at transitions, partial differential equations for generating functions, normal perturbation theory, singular perturbation theory with scaling, numerical computations, and certain matrix methods that combine Perron-Frobenius theory with variational estimates. Applications to experimental results on expected values, variances, and statistical distributions of DNA lesions are briefly outlined. Continuous-time Markov chains are the most systematic of those radiation damage models that treat DSB-DSB interactions within the cell nucleus as homogeneous (e.g., ignore diffusion limitations). They contain virtually all other relevant homogeneous models and semiempirical summaries as special cases, limiting cases, or approximations. However, the Markov models do not seem to be well suited for studying spatial dependence of DSB interactions, which is known to be important in some situations.

Animals↗

PubMed2002

Analysis of the picosecond magneto-optical phenomena in scattering media of biological interest.

The behaviour of a magneto-optically active biological-like medium under picosecond optical excitation is analysed. The new technique is based on the fact that photons trapped in multiple scattering events inside the magneto-optical medium leave the medium with larger induced rotation angles, as they travel longer distances. Two- and three-dimensional displacements of the photons in the medium are separately analysed. The dependence of this effect on the applied magnetic field strength, the value of the magneto-optical constant of the medium and the standard deviation of the statistical distribution of the photons scattered inside the turbid medium are studied. The best values for the magnetic field and optical parameters of the biological medium are proposed for the experimental observation of the picosecond magneto-optical phenomena in scattering media of biological origin. We also make some prospective studies to evaluate the potential application of the magneto-optical effect as a tool for optical tissue biopsy. Values for the optimum magnetic field intensities and for the expected experimental sensitivity in diverse conditions are reported.

Biophysics↗