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PubMed2005

Nematic-nematic phase separation in binary mixtures of thick and thin hard rods: results from Onsager-like theories.

The fundamental nature of the nematic-nematic phase separation in binary mixtures of rigid hard rods is analyzed within the Onsager second-virial theory and the extension of Parsons and Lee which includes a treatment of the higher-body contributions. The particles of each component are modeled as hard spherocylinders of different diameter , but equal length . In the case of a system which is restricted to be fully aligned (parallel rods), we provide an analytical solution for the spinodal boundary for the limit of stability of demixing; only a single region of coexistence bounded at lower pressures (densities) by a critical point is possible for such a system. The full numerical solution with the Parsons-Lee extension also indicates that, depending on the length of the particles, there is a range of values of the diameter ratio where the phase coexistence is closed off by a critical point at lower pressure. A second region of coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" critical point. The two coexistence regions can also merge to give a single region of coexistence extending to very high pressure without a critical point. By including the higher-order contributions to the excluded volume (end effects) in the Onsager theory, we prove analytically that the existence of the lower critical point is a direct consequence of the finite size of the particles. A new analytical equation of state is derived for the nematic phase using the Gaussian approximation. In the case of Onsager limit (infinite aspect ratio), we show that the phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the phase behavior of recent experimental results for mixtures of thin and thick rods of the same length, for which the Onsager and Parsons-Lee theories can provide a qualitative description.

Journal Article↗
PubMed2005

Applying spatial distribution analysis techniques to classification of 3D medical images.

OBJECTIVE: The objective of this paper is to classify 3D medical images by analyzing spatial distributions to model and characterize the arrangement of the regions of interest (ROIs) in 3D space. METHODS AND MATERIAL: Two methods are proposed for facilitating such classification. The first method uses measures of similarity, such as the Mahalanobis distance and the Kullback-Leibler (KL) divergence, to compute the difference between spatial probability distributions of ROIs in an image of a new subject and each of the considered classes represented by historical data (e.g., normal versus disease class). A new subject is predicted to belong to the class corresponding to the most similar dataset. The second method employs the maximum likelihood (ML) principle to predict the class that most likely produced the dataset of the new subject. RESULTS: The proposed methods have been experimentally evaluated on three datasets: synthetic data (mixtures of Gaussian distributions), realistic lesion-deficit data (generated by a simulator conforming to a clinical study), and functional MRI activation data obtained from a study designed to explore neuroanatomical correlates of semantic processing in Alzheimer's disease (AD). CONCLUSION: Performed experiments demonstrated that the approaches based on the KL divergence and the ML method provide superior accuracy compared to the Mahalanobis distance. The later technique could still be a method of choice when the distributions differ significantly, since it is faster and less complex. The obtained classification accuracy with errors smaller than 1% supports that useful diagnosis assistance could be achieved assuming sufficiently informative historic data and sufficient information on the new subject.

Algorithms↗
PubMed2001

Algebraic geometrical methods for hierarchical learning machines.

Hierarchical learning machines such as layered perceptrons, radial basis functions, Gaussian mixtures are non-identifiable learning machines, whose Fisher information matrices are not positive definite. This fact shows that conventional statistical asymptotic theory cannot be applied to neural network learning theory, for example either the Bayesian a posteriori probability distribution does not converge to the Gaussian distribution, or the generalization error is not in proportion to the number of parameters. The purpose of this paper is to overcome this problem and to clarify the relation between the learning curve of a hierarchical learning machine and the algebraic geometrical structure of the parameter space. We establish an algorithm to calculate the Bayesian stochastic complexity based on blowing-up technology in algebraic geometry and prove that the Bayesian generalization error of a hierarchical learning machine is smaller than that of a regular statistical model, even if the true distribution is not contained in the parametric model.

Algorithms↗
PubMed2005

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid.

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.

Journal Article↗
PubMed2003

Brownian dynamics simulations of aging colloidal gels.

The aging of colloidal gels is investigated using very long duration Brownian dynamics simulations. The Asakura-Oosawa description of the depletion interaction is used to model a simple colloid polymer mixture. Several regimes are identified during gel formation. The intermediate scattering function displays a double decay characteristic of systems where some kinetic processes are frozen. The beta relaxation at short times is explained in terms of the Krall-Weitz model for the decorrelation due to the elastic modes present. The alpha relaxation at long times is well described by a stretched exponential, showing a wide spectrum of relaxation times for which the q dependence is tau(alpha)=q(-2.2), lower than for diffusion. For the shortest waiting times, a combination of two stretched exponentials is used, suggesting a bimodal distribution. The extracted relaxation times vary with waiting time as tau(alpha)=tau(0.66)(w), more slowly than in the simple aging case. The real space displacements are found to be strongly non-Gaussian, correlated in space and time. We were unable to find clear evidence that the gel aging was driven by internal stresses. Rather, we hypothesize that in this case of weakly interacting gels, the aging behavior arises due to the thermal diffusion of strands, constrained by the percolating network, which ruptures discontinuously. Although the mechanisms differ, the similarity of some of the results to aging of glasses is striking.

Journal Article↗
PubMed1991

Protein dynamics. Comparative investigation on heme-proteins with different physiological roles.

We report the low temperature carbon monoxide recombination kinetics after photolysis and the temperature dependence of the visible absorption spectra of the isolated alpha SH-CO and beta SH-CO subunits from human hemoglobin A in ethylene glycol/water and in glycerol/water mixtures. Kinetic measurements on sperm whale (Physeter catodon) myoglobin and previously published optical spectroscopy data on the latter protein and on human hemoglobin A, in both solvents, (Cordone, L., A. Cupane, M. Leone, E. Vitrano, and D. Bulone. 1988. J. Mol. Biol. 199:312-218) are taken as reference. Low temperature flash photolysis data are analyzed within the multiple substates model proposed by Frauenfelder and co-workers (Austin, R. H., K. W. Beeson, L. Eisenstein, H. Frauenfelder, and I. C. Gunsalus. 1975. Biochemistry. 14:5355-5373). Within this model a distribution of activation enthalpies for ligand binding accounts for the structural heterogeneity of the protein, while the preexponential factor, containing also the entropic contribution to the free energy of the process, is considered to be constant for all conformational substates. Optical spectra are deconvoluted in gaussian components and the temperature dependence of the moments of the resulting bands is analyzed, within the harmonic Frank-Condon approximation, to obtain information on the stereodynamic properties of the heme pocket. The kinetic and spectral parameters thus obtained are found to be protein dependent also with respect to their sensitivity to changes in the composition of the external medium. A close correlation between the kinetic and spectral features is observed for the proteins examined under all experimental conditions studied. The results reported are discussed in terms of differences in the heme pocket structure and in the conformational heterogeneity among the various proteins, as related to their different capability to accommodate constraints imposed by the external medium.

Animals↗
PubMed2003

Simulation study of nonergodicity transitions: gelation in colloidal systems with short-range attractions.

Computer simulations were used to study the gel transition occurring in colloidal systems with short-range attractions. A colloid-polymer mixture was modeled and the results were compared with mode coupling theory (MCT) expectations and with the results for other systems (hard-spheres system and Lennard-Jones system). The self-intermediate scattering function and the mean squared displacement were used as the main dynamical quantities. Two different colloid packing fractions have been studied. For the lower packing fraction, alpha-scaling holds and the wave-vector analysis of the correlation function shows that gelation is a regular nonergodicity transition within MCT. The leading mechanism for the novel nonergodicity transition is identified as the bond formation caused by the short-range attraction. The time scale and diffusion coefficient also show qualitatively the expected behavior, although different exponents are found for the power-law divergences of these two quantities. The non-Gaussian parameter was also studied and a very large correction to Gaussian behavior was found. The system with higher colloid packing fraction shows indications of a nearby high-order singularity, causing alpha scaling to fail, but the general expectations for nonergodicity transitions still hold.

Journal Article↗
PubMed2003

Application of fractal and morphological methods in radioecology.

Effective management of radioactive contamination requires comprehensive knowledge of pollutants' characteristics. The complicated character of the problem is due to a number of issues, such as the very wide range of contamination, the presence of a mixture of radioactive isotopes, the highly variable diffusion of radionuclides in soil, water, and air, and the effect of climatic conditions. The resultant field has an irregular mosaic structure, which restricts the choice of measurement methods and data processing. In view of this, application of classical statistics techniques is often inappropriate in modeling such an environment. Application of the tools of fractal and stochastic geometry provides a good insight and helps to distinguish between distribution characteristics of natural and man-made isotopes. Several techniques are implemented to determine scaling aspects of contaminated fields. The discovery of multifractal scaling leads to the hierarchical structure of contamination spots on different scales and intensity and places restrictions on the measurement net for detecting anomalies. The method of stochastic geometry further demonstrates that topological characteristics of contamination fields differ from those of the Gaussian fields and the topology of man-made isotopes differs from natural ones.

Air Pollutants, Radioactive↗
PubMed1996

Quantal components of spontaneous excitatory junction potentials at visualised varicosities.

The electrical signs of spontaneous transmitter release were recorded with an extracellular electrode from single visualized sympathetic varicosities on the mouse vas deferens. Ultrastructural examination of these varicosities with the electron microscope showed that they formed close-contacts with smooth muscle cells. Amplitude-frequency histograms of the spontaneous excitatory junction potentials (SEJPs) were constructed in order to determine the statistical nature of spontaneous transmitter release from a varicosity. SEJP histograms often possessed several peaks. Statistical tests showed that these were separate modes in the histograms indicating that the SEJPs were composed of subunits. The SEJP histograms were described by a mixture of distributions in which the components were identified as quanta and there was a Poisson release of quanta. The second mode in the SEJP histograms was sometimes twice that of the first mode but generally greater, suggesting a potentiation of the effects of one quantum released nearly simultaneously with another quantum. The components in the SEJP histograms were well fitted by either a Gaussian or a gamma distribution indicating that the quantum of transmitter could be described as a Gaussian or gamma variate.

Animals↗
PubMed2002

Comparison of three methods for estimating the standard error of the area under the curve in ROC analysis of quantitative data.

RATIONALE AND OBJECTIVES: Several methods have been proposed for estimating the standard error (SE) of the area under the curve (AUC) in receiver operating characteristic analysis. The authors examined the validity of three methods--the LABROC procedure, exponential approximation, and the method of DeLong et al (purely nonparametric)--for estimating the SE of the AUC in receiver operating characteristic analysis of quantitative diagnostic data. MATERIALS AND METHODS: The authors conducted a broad numerical investigation to assess how to estimate the SE of AUC in various configurations of binormal and nonbinormal pairs of distributions, in which one or both pair members were mixtures of Gaussian distributions (the samples included 100 in the diseased group and 100 in the nondiseased group). RESULTS: The authors found that exponential approximation of the SE of AUC slightly underestimates the observed SE of a nonparametric estimate of the AUC when the ratio of the standard deviation of distributions for diseased to nondiseased populations was greater than 2. With binormal data the observed SE tended to be smaller with the LABROC procedure (semiparametric) than with the method of DeLong et al, but the LABROC procedure yields more conservative estimates of SE with nonbinormal data. In particular, with bimodal data it often produces a more conservative (ie, larger) estimate of the actual (observed) fluctuation. CONCLUSION: Overall, the LABROC procedure and the method of DeLong et al yielded very close estimates of the SE of AUC, even with data generated from a nonbinormal model. The choice between these two methods can be based on users' preferences and practicality.

Area Under Curve↗
PubMed2005

Recognizing partially occluded, expression variant faces from single training image per person with SOM and soft kappa-NN ensemble.

Most classical template-based frontal face recognition techniques assume that multiple images per person are available for training, while in many real-world applications only one training image per person is available and the test images may be partially occluded or may vary in expressions. This paper addresses those problems by extending a previous local probabilistic approach presented by Martinez, using the self-organizing map (SOM) instead of a mixture of Gaussians to learn the subspace that represented each individual. Based on the localization of the training images, two strategies of learning the SOM topological space are proposed, namely to train a single SOM map for all the samples and to train a separate SOM map for each class, respectively. A soft kappa nearest neighbor (soft kappa-NN) ensemble method, which can effectively exploit the outputs of the SOM topological space, is also proposed to identify the unlabeled subjects. Experiments show that the proposed method exhibits high robust performance against the partial occlusions and variant expressions.

Algorithms↗
PubMed2002

Micromechanics of isolated sickle cell hemoglobin fibers: bending moduli and persistence lengths.

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.

Anemia, Sickle Cell↗
PubMed2005

Infrared spectroscopy of acetone-methanol liquid mixtures: hydrogen bond network.

Acetone and methanol mixtures covering the whole solubility range are studied by Fourier transform infrared attenuated total reflectance spectroscopy. The strong bathochromic shifts observed on methanol OH and acetone CO stretch IR bands are related to hydrogen bonds between these groups. Factor analysis separates the spectra into four acetone and four methanol principal factors. A random molecular model developed for the acetone-water system [Max and Chapados, J. Chem. Phys. 119, 5632 (2003); 120, 6625 (2004)] was modified for the acetone-methanol system. This model, which takes into account H bonds accepted by methanol and acetone, is made up of 12 methanol and 11 acetone species. The 23 species abundances are regrouped according to evolving patterns or spectral similarities to compare them to the eight experimental factors. Methanol acetone mixtures are almost but not exactly random: the methanol oxygen atoms have stronger capacities than acetone to accept H bonds from methanol in the proportion 1.5 to 1. Since oxygen atoms are in excess, all labile hydrogen atoms will form H bonds. As acetone is added to methanol, its OH stretch band blueshifts as the number of accepted H bonds decreases. When methanol gives one H bond and accepts one, an H-bonding network is formed that was coined "chained organization." However, the acetone molecules do not sequester any methanol molecules by breaking or increasing the H-bond methanol network. Similarly, the methanol molecules do not sequester any acetone molecules. Consequently no acetone-methanol complex is formed in the mixtures. Gaussian simulation of the four principal factors in the methanol OH stretch region gave three distinct absorption regimes consisting of the OH stretch bands and their satellites that are identified as MeOH(1), MeOH(2), and MeOH(3) (subscript indicates the number of H, covalent and H bond, which surround the oxygen). These regimes are related to those identified in the water-acetone system as OH(2), OH(3), and OH(4).

Journal Article↗
PubMed1994

Practical guidance for testing the accuracy of deconvolution results from quantal analysis.

A Monte Carlo study was carried out to test the reliability of the Maximum Likelihood Estimator (MLE) approach for quantal analysis. This widely used statistical method was applied to extract a finite mixture of Gaussian distributions from simulated data. The data were generated by convolving a distribution of discrete amplitude steps (multiples of a unitary step Q) with Gaussian noise of various standard deviations (sigma n). Our results offer practical guidance on when to use the MLE, taking into account the determining parameters: signal to noise ratio (Q/sigma n, the most important parameter), number of samples collected and the number of components (k). For a given set of parameters the algorithm always converged to the "true" values, never converged to the "true" values or converged in only a fraction of cases to the "true" values. The behavior of the fitting routine in the parameter space is displayed in contour plots. These contour plots can be used as a guide to test the accuracy of deconvolution results.

Computer Simulation↗
PubMed2004

Developing optimal non-linear scoring function for protein design.

UNLABELLED: Motivation. Protein design aims to identify sequences compatible with a given protein fold but incompatible to any alternative folds. To select the correct sequences and to guide the search process, a design scoring function is critically important. Such a scoring function should be able to characterize the global fitness landscape of many proteins simultaneously. RESULTS: To find optimal design scoring functions, we introduce two geometric views and propose a formulation using a mixture of non-linear Gaussian kernel functions. We aim to solve a simplified protein sequence design problem. Our goal is to distinguish each native sequence for a major portion of representative protein structures from a large number of alternative decoy sequences, each a fragment from proteins of different folds. Our scoring function discriminates perfectly a set of 440 native proteins from 14 million sequence decoys. We show that no linear scoring function can succeed in this task. In a blind test of unrelated proteins, our scoring function misclassfies only 13 native proteins out of 194. This compares favorably with about three-four times more misclassifications when optimal linear functions reported in the literature are used. We also discuss how to develop protein folding scoring function.

Algorithms↗
PubMed2000

On-line EM algorithm for the normalized gaussian network.

A normalized gaussian network (NGnet) (Moody & Darken, 1989) is a network of local linear regression units. The model softly partitions the input space by normalized gaussian functions, and each local unit linearly approximates the output within the partition. In this article, we propose a new on-line EMalgorithm for the NGnet, which is derived from the batch EMalgorithm (Xu, Jordan, &Hinton 1995), by introducing a discount factor. We show that the on-line EM algorithm is equivalent to the batch EM algorithm if a specific scheduling of the discount factor is employed. In addition, we show that the on-line EM algorithm can be considered as a stochastic approximation method to find the maximum likelihood estimator. A new regularization method is proposed in order to deal with a singular input distribution. In order to manage dynamic environments, where the input-output distribution of data changes over time, unit manipulation mechanisms such as unit production, unit deletion, and unit division are also introduced based on probabilistic interpretation. Experimental results show that our approach is suitable for function approximation problems in dynamic environments. We also apply our on-line EM algorithm to robot dynamics problems and compare our algorithm with the mixtures-of-experts family.

Algorithms↗
PubMed2006

Fluorescence recovery under decaying photobleaching irradiation: concept and experiment.

A novel modification of photobleaching method for measurement of lateral diffusion is developed. In this approach fluorescence recovery kinetics is measured under decaying photobleaching irradiation, termed as fluorescence recovery under decaying photobleaching (FRDP). The time evolution of fluorescence intensity normalized to input irradiation starts from the photobleaching kinetics and transforms into the kinetics of fluorescence recovery at a later stage resulting in appearance of minimum. The analytical solution for the kinetics of fluorescence for Gaussian lineshape of laser beam and hyperbolic decay of irradiation in the first order approximation on bleaching rate was obtained. The accuracy of the analytical function was evaluated with exact numerical solution computed with finite differentiates method. The FRDP method was successfully applied to fluorescein solution in the glycerol/water mixture (80%) under various experimental settings using home-made experimental set-up. The FRDP approach demonstrated 25-30 fold enhancement in signal intensity over classical fluorescence recovery after photobleaching (FRAP) method at 3-5 fold increase in total irradiation. Among other advantages of the FRDP is the opportunity to perform measurements on varying time scales under constant size of the bleaching spot, including "safe" long time measurements. The potential extra advantage of FRDP method for analysis of complex diffusion in the biological system is discussed.

Fluorescence Recovery After Photobleaching↗
PubMed2007

Nonparametric estimation of the mean function of a stochastic process with missing observations.

In an attempt to identify similarities between methods for estimating a mean function with different types of response or observation processes, we explore a general theoretical framework for nonparametric estimation of the mean function of a response process subject to incomplete observations. Special cases of the response process include quantitative responses and discrete state processes such as survival processes, counting processes and alternating binary processes. The incomplete data are assumed to arise from a general response-independent observation process, which includes right-censoring, interval censoring, periodic observation, and mixtures of these as special cases. We explore two criteria for defining nonparametric estimators, one based on the sample mean of available data and the other inspired by the construction of Kaplan-Meier (or product-limit) estimator [J. Am. Statist. Assoc. 53 (1958) 457] for right-censored survival data. We show that under regularity conditions the estimated mean functions resulting from both criteria are consistent and converge weakly to Gaussian processes, and provide consistent estimators of their covariance functions. We then evaluate these general criteria for specific responses and observation processes, and show how they lead to familiar estimators for some response and observation processes and new estimators for others. We illustrate the latter with data from an recently completed AIDS clinical trial.

Acquired Immunodeficiency Syndrome↗