Obtaining the Morse parameter for large bond-stretching using Murrell-Sorbie parameters

Although the second derivative approach has been shown to provide good parameter relationships between any two interatomic potential functions, these relations are valid only at and near the equilibrium point. Arising from the significant discrepancy between connected potential functions for large stretching of covalent bonds by the second derivative approach, an integral approach is developed herein. By equating interatomic energy integral from equilibrium to bond dissociation, the overall discrepancy is minimized for that range between the Morse and Murrell-Sorbie potential functions. Plotted results reveal two observations. First of all, the second derivative approach is appropriate for bond compression and infinitesimal bond stretching, while the integral approach is more suitable when the extent of bond stretching is significant. Secondly, the Morse function exactly fits the Murrell-Sorbie curve when the Morse shape parameters based on the second derivative and integral approaches are equal. Hence a criterion for determining the accuracy level of Murrell-Sorbie parameters for conversion to Morse parameter is established. Finally, a demonstration was made for cases where a clear discrepancy was observed in the potential energy curves. It was found that the integral approach gives a more conservative and more realistic interatomic force curve than those of derivative approach. Figure Morse potential force using Murrell-Sorbie parameters     

Shrinkage Pre-Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student-t Errors

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.     

Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments

An experiment design procedure is proposed for nonlinear parameter estimation studies that formally incorporates prior parameter uncertainty. The design criterion derives from information theory considerations and involves an asymptotic interpretation of the expected posterior information provided by an experiment. A pharmacokinetic sample schedule design problem is used to illustrate and evaluate this information theoretic design strategy. The model considered is commonly used to describe the plasma concentration of a drug following its oral administration. The limitations and advantages of the proposed design procedure are discussed in relation to other previously reported design techniques for incorporating parameter uncertainty.     

Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.     

Studies in stochastic learning theory: I path-dependent linear models for experimenter-subject controlled experiments

The derivation of learning models relative to choice behavior in experimenter-subject controlled experiments with two outcomes (right or wrong) is considered from the point of view that any such model must satisfy a criterion of optimality. The criterion adopted for investigation, termed optimal asymptotic behavior, is that of the subject asymptotically learning which of the alternatives has the greater probability of being correct. A class of path-dependent linear models is posed as possible candidates. It is shown that no members of this class satisfy the criterion although two of them approach it by making a learning parameter small enough. The possible implications of this are discussed.     

Further studies on membrane transport with time delay

A theory of cell membrane transport with a time delay which predicts under certain conditions overshoot or oscillatory permeation (Ohshima and Kondo, Biophys. Chem. 33 (1989) 303), is extended with the introduction of a parameter expressing a fraction of solutes inside the cell interior that suffer time delay. It is found that criterion for oscillation depends strongly on this parameter. Results will also be presented for the case of an exponential-type distribution of the delay time.     

Parameter estimation of a monod-type model. Part II: Use of a neural network with associative memories

Summary On the basis of a previous study related with parameter identifiability and sensitivity analysis of a Monod-type model, a parameter estimation method based on Artificial Neural Networks (ANN) with Associative Memories (AMs) is presented. A combination of an iterative procedure and a convergence index given by AMs allows to confirm the nature of relations existing between state variables and parameters which were found in the first part of the study. The convergence criterion is particularly well adapted to showing various influences of state variables on parameter estimation of such a model.     

Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

The problem of evaluating the goodness of the predictive distributionsof hierarchical Bayesian and empirical Bayes models is investigated.A Bayesian predictive information criterion is proposed as anestimator of the posterior mean of the expected loglikelihoodof the predictive distribution when the specified family ofprobability distributions does not contain the true distribution.The proposed criterion is developed by correcting the asymptoticbias of the posterior mean of the loglikelihood as an estimatorof its expected loglikelihood. In the evaluation of hierarchicalBayesian models with random effects, regardless of our parametricfocus, the proposed criterion considers the bias correctionof the posterior mean of the marginal loglikelihood becauseit requires a consistent parameter estimator. The use of thebootstrap in model evaluation is also discussed.     

The refined crystal structure of ribonuclease A at 2.0 A resolution

This paper describes the structure of bovine pancreatic ribonuclease A, refined by a restrained parameter least squares procedure at 2.0 A resolution, and rebuilt using computer graphics. The final agreement factor (formula see text) is 0.159. The positions of the 951 main chain atoms have been determined with an estimated accuracy of 0.17 A. In addition, the model includes a phosphate group in the active site and 176 waters, many of them with partial occupancy. The bond lengths in the refined structure of RNase A differ from the ideal values by an overall root mean square deviation of 0.022 A; the corresponding value for angle distances is 0.06 A. The root mean square deviation of planar atoms from ideality is 0.017 A, and root mean square deviation of the peptide torsion angles from 180 degrees is 3.4 degrees. The model is in good agreement with the final difference Fourier maps. Two active site histidines, His 12 and His 119, form hydrogen bonds to the phosphate ion. His 119 is also hydrogen bonded to the carboxyl of ASp 121 and His 12 to the carbonyl of Thr 45. The structure of the RNase A is very similar to that of RNase S, particularly in the active site region. The root mean square discrepancy of all atoms from residues 1 to 16 and 24 to 123 is 1.06 A and the root mean square discrepancy for the active site region is 0.6 A.     

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

A precise definition of the basic reproduction number, , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if , then the disease free equilibrium is locally asymptotically stable; whereas if , then it is unstable. Thus, is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for near one. This criterion, together with the definition of , is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models. The results are significant for disease control.     

The causal theory of the resting potential of cells

In this pedagogical article the causal theory of the resting potential of cells is presented, which for given extracellular ion concentrations predicts the intracellular ones simultaneously with the resting potential. In addition to the Na, K-pump, fixed charges on the membrane surfaces are taken into account. The equation determining the resting potential in the causal theory suggests a new explanation of the genesis of the resting potential. The usual criterion for an ion pump to be electrogenic is not relevant for the whole of the resting potential, and may therefore be misleading. The physical meaning of the Goldman-Hodgkin-Katz formula for the membrane potential as a diffusion potential is also explained and tested with numbers for the giant axon of the squid. A significant discrepancy between theory and experiment is found which calls for an experimental re-examination of the constitutive equations for passive potassium and sodium currents.     

Modeling of weak blast wave propagation in the lung

Blast injuries of the lung are the most life-threatening after an explosion. The choice of physical parameters responsible for trauma is important to understand its mechanism. We developed a one-dimensional linear model of an elastic wave propagation in foam-like pulmonary parenchyma to identify the possible cause of edema due to the impact load. The model demonstrates different injury localizations for free and rigid boundary conditions. The following parameters were considered: strain, velocity, pressure in the medium and stresses in structural elements, energy dissipation, parameter of viscous criterion. Maximum underpressure is the most suitable wave parameter to be the criterion for edema formation in a rabbit lung. We supposed that observed scattering of experimental data on edema severity is induced by the physiological variety of rabbit lungs. The criterion and the model explain this scattering. The model outlines the demands for experimental data to make an unambiguous choice of physical parameters responsible for lung trauma due to impact load.     

Statistical evaluation of ion-channel gating models based on distributions of log-likelihood ratios

The distributions of log-likelihood ratios (DeltaLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Xi, full model; Xi(R), submodel) were studied both theoretically and using simulated data. When Xi is true, DeltaLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When Xi(R) is true and corresponds to a distinct point in full parameter space, DeltaLL is Gamma-distributed (2DeltaLL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, Xi(R) corresponds to an infinite set of points in parameter space. The distribution of DeltaLL is a mixture of two components, one identically zero, the other approximated by a Gamma-distribution. This empirical distribution of DeltaLL, assuming Xi(R), allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Xi, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and DeltaLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of DeltaLL when Xi or Xi(R) is true.     

Scale-up of antibiotic fermentations by control of oxygen utilization

Oxygen Utilization as a scale-up parameter is evaluated in two antibiotic-producing fermentations. This method of scale-up was used in tank-to-tank and in flash-to-flash scale-up studies. Antibiotic yields and cell weight trends were generally duplicated in the replicate runs, with some discrepancy noted in chlortetracycline yields at high aeration levels. The apparatus for measuring oxygen consumption rates and for automatically controlling oxygen utilization, according to a predetermined pattern, is described.     

An investigation of the effect of radioactive labeling of DNA on excision repair in UV-irradiated human fibroblasts.

Previous studies on the kinetics of thymine dimer excision and unscheduled DNA synthesis in UV-irradiated human fibroblasts showed a significant discrepancy in these two parameters (Ehmann et al., 1978. Biophys. J. 22: 249). In the present study we have investigated the effect of the level of the radioactive isotope used for labeling cells on the kinetics of a parameter that directly measures thymine dimer excision. We find no significant differences in the kinetics of this parameter in cells lightly or heavily labeled with radioactive thymidine.     

Deciphering network community structure by surprise

The analysis of complex networks permeates all sciences, from biology to sociology. A fundamental, unsolved problem is how to characterize the community structure of a network. Here, using both standard and novel benchmarks, we show that maximization of a simple global parameter, which we call Surprise (S), leads to a very efficient characterization of the community structure of complex synthetic networks. Particularly, S qualitatively outperforms the most commonly used criterion to define communities, Newman and Girvan's modularity (Q). Applying S maximization to real networks often provides natural, well-supported partitions, but also sometimes counterintuitive solutions that expose the limitations of our previous knowledge. These results indicate that it is possible to define an effective global criterion for community structure and open new routes for the understanding of complex networks.     

On a criterion for survival of species in models governed by difference equations

The difficulty of deciding on the survival of species in models governed by difference equations is pointed out. We show that a recently proposed criterion may overestimate the range of parameter values for which survival is assured.     

On the sensitive dependence on initial conditions of the dynamics of networks of spiking neurons

We have previously formulated an abstract dynamical system for networks of spiking neurons and derived a formal result that identifies the criterion for its dynamics, without inputs, to be “sensitive to initial conditions”. Since formal results are applicable only to the extent to which their assumptions are valid, we begin this article by demonstrating that the assumptions are indeed reasonable for a wide range of networks, particularly those that lack overarching structure. A notable aspect of the criterion is the finding that sensitivity does not necessarily arise from randomness of connectivity or of connection strengths, in networks. The criterion guides us to cases that decouple these aspects: we present two instructive examples of networks, one with random connectivity and connection strengths, yet whose dynamics is insensitive, and another with structured connectivity and connection strengths, yet whose dynamics is sensitive. We then argue based on the criterion and the gross electrophysiology of the cortex that the dynamics of cortical networks ought to be almost surely sensitive under conditions typically found there. We supplement this with two examples of networks modeling cortical columns with widely differing qualitative dynamics, yet with both exhibiting sensitive dependence. Next, we use the criterion to construct a network that undergoes bifurcation from sensitive dynamics to insensitive dynamics when the value of a control parameter is varied. Finally, we extend the formal result to networks driven by stationary input spike trains, deriving a superior criterion than previously reported. Action Editor: John Rinzel     

Clustering in linear‐mixed models with a group fused lasso penalty

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear‐mixed models that are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose, an EM algorithm‐based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.     

Focused information criterion on predictive models in personalized medicine

Instead of assessing the overall fit of candidate models like the traditional model selection criteria, the focused information criterion focuses attention directly on the parameter of the primary interest and aims to select the model with the minimum estimated mean squared error for the estimate of the focused parameter. In this article we apply the focused information criterion for personalized medicine. By using individual‐level information from clinical observations, demographics, and genetics, we obtain the personalized predictive models to make the prognosis and diagnosis individually. The consideration of the heterogeneity among the individuals helps reduce the prediction uncertainty and improve the prediction accuracy. Two real data examples from biomedical research are studied as illustrations.