random dynamics of the hodgkin huxley neuron model noise can alter the response of neurons enhancing their ability to detect weak inputs we analyze how the hodgkin huxley equations a canonical neuron model respond to white noise stimulation we show that this model possesses a stochastic attractor reduced to a unique stochastic equilibrium point that attracts all trajectories

an approximate analytic solution method for the biharmonic problem a method is presented for the solution of the biharmonic equation through the use of a combination of polynomial and eigenfunction solutions results are presented comparing the method with an exact solution excellent agreement is obtained for economical solution representations calculations and comparison with established results of the displacement of an elastic plate under a uniform applied load are presented further results are presented of the calculation of zero reynolds number flow in a driven cavity

dynamics of moments of fitzhugh nagumo neuronal models and stochastic bifurcations for the study of the behavior of noisy neuronal models rodriguez and tuckwell have introduced an elegant and systematic method which consists of replacing the system of stochastic differential equations with a system of deterministic equations representing the dynamics of the means variances and covariance of the state variables r rodriguez and h c tuckwell phys rev e 54 5585 1996 in this work we first report a modification of their method in the case of the fitzhugh nagumo model which enhances the accuracy of the approximation without including higher order moments this method is then combined with a self consistency argument in order to better characterize the behavior of the underlying stochastic processes through the computation of approximate auto and cross correlation functions of the state variables finally we argue that the moments equations can also reveal the existence of stochastic bifurcations i e qualitative changes in the dynamics of stochastic systems

stochastic methods for epidemic models we present stochastic methods for computation of influenza transmission models we use the moment closure method that reduces computational load much we find quantitative differences between deterministic and stochastic solutions we investigate the impact of various vaccination and antiviral treatment scenarios in this paper we present stochastic methods for computation of influenza transmission models first seir type deterministic epidemiological models are revisited and stochastic modeling for those models are introduced the main motivation of our work is to present computational methods of the stochastic epidemic models in particular the moment closure method mcm is developed for some influenza models and compared with the results under the standard stochastic simulation algorithm ssa all epidemic outcomes including the peak size the peak timing and the final epidemic size of both methods are in a good agreement however the mcm has reduced the computational time and costs significantly next the mcm has been employed to model the 2009 h1n1 influenza transmission dynamics in south korea the influenza outcomes are compared under the standard deterministic approach and the stochastic approach mcm our results show that there is a considerable discrepancy between the results of stochastic and deterministic models especially when a small number of infective individuals is present initially lastly we investigate the effectiveness of control policies such as vaccination and antiviral treatment under various scenarios

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

a fast algorithm for simulating vesicle flows in three dimensions vesicles are locally inextensible fluid membranes that can sustain bending in this paper we extend the study of veerapaneni et al s k veerapaneni d gueyffier g biros d zorin a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows journal of computational physics 228 19 2009 7233 7249 to general non axisymmetric vesicle flows in three dimensions although the main components of the algorithm are similar in spirit to the axisymmetric case spectral approximation in space semi implicit time stepping scheme important new elements need to be introduced for a full 3d method in particular spatial quantities are discretized using spherical harmonics and quadrature rules for singular surface integrals need to be adapted to this case an algorithm for surface reparameterization is needed to ensure stability of the time stepping scheme and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs to characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi implicit time stepping scheme we perform a spectral analysis of the evolution operator on the unit sphere by introducing these algorithmic components we obtain a time stepping scheme that circumvents the stability constraint on the time step and achieves spectral accuracy in space we present results to analyze the cost and convergence rates of the overall scheme to illustrate the applicability of the new method we consider a few vesicle flow interaction problems a single vesicle in relaxation sedimentation shear flows and many vesicle flows

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

improving power in small sample longitudinal studies when using generalized estimating equations generalized estimating equations gee are often used for the marginal analysis of longitudinal data although much work has been performed to improve the validity of gee for the analysis of data arising from small sample studies little attention has been given to power in such settings therefore we propose a valid gee approach to improve power in small sample longitudinal study settings in which the temporal spacing of outcomes is the same for each subject specifically we use a modified empirical sandwich covariance matrix estimator within correlation structure selection criteria and test statistics use of this estimator can improve the accuracy of selection criteria and increase the degrees of freedom to be used for inference the resulting impacts on power are demonstrated via a simulation study and application example copyright 2016 john wiley sons ltd

the effect of noise on β cell burst period bursting electrical behavior is commonly observed in a variety of nerve and endocrine cells including that in electrically coupled cells located in intact pancreatic islets however individual cells usually display either spiking or very fast bursting behavior and the difference between isolated and coupled cells has been suggested to be due to stochastic fluctuations of the plasma membrane ion channels which are supposed to have a stronger effect on single cells than on cells situated in clusters the channel sharing hypothesis this effect of noise has previously been studied using numerical simulations we show here how the application of two recent methods allows an analytic treatment of the stochastic effects on the location of the saddle node and homoclinic bifurcations which determine the burst period thus the stochastic system can be analyzed similarly to the deterministic system but with a quantitative description of the effect of noise this approach supports previous investigations

sinc galerkin method for solving biharmonic problems there are many techniques available to numerically solve the biharmonic equation in this paper we show that the sinc galerkin method is a very effective tool in numerically solving this equation hermite interpolation is used to treat the nonhomogeneous boundary conditions our method is tested on examples and comparisons with other methods are made it is shown that the sinc galerkin method yields good results even when singularities occur at the boundaries

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks dynamical stochastic models of single neurons and neural networks often take the form of a system of n 2 coupled stochastic differential equations we consider such systems under the assumption that third and higher order central moments are relatively small in the general case a system of 1 n n13 generally nonlinear coupled ordinary differential equations holds for the approximate means variances and covariances for the general linear system the solutions of these equations give exact results this is illustrated in a simple case generally the moment equations can be solved numerically results are given for a spiking fitzhugh nagumo model neuron driven by a current with additive white noise differential equations are obtained for the means variances and covariances of the dynamical variables in a network of n connected spiking neurons in the presence of noise s1063 651x 96 03511 8 pacs number s 87 10 1e 05 40 1j 02 50 2r

mean field approximation of two coupled populations of excitable units the analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of n stochastic excitable units each is performed by studying an approximate system obtained by replacing each population with the corresponding mean field model in the exact system one has the units within an ensemble communicating via the time delayed linear couplings whereas the interensemble terms involve the nonlinear time delayed interaction mediated by the appropriate global variables the aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system governed by a set of 4n stochastic delay differential equations for the microscopic dynamics can accurately be reproduced by a flow containing just four deterministic delay differential equations which describe the evolution of the mean field based variables in particular the considered issues include determining the parameter domains where the stationary state is stable the scenarios for the onset and the time delay induced suppression of the collective mode as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state we show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations like those with symmetrical or asymmetrical interpopulation couplings

akaike s information criterion in generalized estimating equations correlated response data are common in biomedical studies regression analysis based on the generalized estimating equations gee is an increasingly important method for such data however there seem to be few model selection criteria available in gee the well known akaike information criterion aic cannot be directly applied since aic is based on maximum likelihood estimation while gee is nonlikelihood based we propose a modification to aic where the likelihood is replaced by the quasi likelihood and a proper adjustment is made for the penalty term its performance is investigated through simulation studies for illustration the method is applied to a real data set

the impact of covariance misspecification in multivariate gaussian mixtures on estimation and inference an application to longitudinal modeling multivariate gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes when the outcome is a vector of repeated measurements taken on the same subject there is often inherent dependence between observations however a common covariance assumption is conditional independence that is given the mixture component label the outcomes for subjects are independent in this paper we study through asymptotic bias calculations and simulation the impact of covariance misspecification in multivariate gaussian mixtures although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified we also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice copyright 2013 john wiley sons ltd

moment dynamics for gene regulation with rational rate laws this aim of this paper is mainly to investigate the performance of two typical moment closure schemes in gene regulatory master equations of rational rate laws when the reaction rate is polynomial the error bounds between the authentic and approximate moments obtained by schemes of gaussian moment closure and log normal moment closure are explicitly given when the reaction rate is not polynomial it is shown that the two schemes both behave well in the absence of active inactive state switch but in the presence of active inactive state switch the log normal closure scheme is far superior to the gaussian closure scheme in capturing the asymptotic ensemble statistics moreover the accuracy of the log normal closure method is further confirmed by steady state analytic results and the conditional gaussian closure method it is also disclosed that optimal negative feedback exists in suppressing protein noise in the presence of the on off switch control

a phase field model for vesicle substrate adhesion in this paper a phase field model is developed for vesicle adhesion involving complex substrate and vesicle geometries the model takes into account an adhesion potential that depends on the distance of vesicle to the substrate a variational problem is solved in a 3d computational domain by minimizing the contribution of bending elastic energy and the adhesion energy under the constraints of total surface area and volume described via a phase function an adaptive finite element method is used to efficiently compute the numerical solutions of the model the computational results are validated through comparison of several axisymmetric shapes with the sharp interface ode solution moreover we compute shapes for non axisymmetric situations to support the observation that concave substrates favor adhesion

a determinant based criterion for working correlation structure selection in generalized estimating equations in generalized estimating equations gee the correlation between the repeated observations on a subject is specified with a working correlation matrix correct specification of the working correlation structure ensures efficient estimators of the regression coefficients among the criteria used in practice for selecting working correlation structure rotnitzky jewell quasi information criterion qic and correlation information criterion cic are based on the fact that if the assumed working correlation structure is correct then the model based naive and the sandwich robust covariance estimators of the regression coefficient estimators should be close to each other the sandwich covariance estimator used in defining the rotnitzky jewell qic and cic criteria is biased downward and has a larger variability than the corresponding model based covariance estimator motivated by this fact a new criterion is proposed in this paper based on the bias corrected sandwich covariance estimator for selecting an appropriate working correlation structure in gee a comparison of the proposed and the competing criteria is shown using simulation studies with correlated binary responses the results revealed that the proposed criterion generally performs better than the competing criteria an example of selecting the appropriate working correlation structure has also been shown using the data from madras schizophrenia study

the analysis of binary longitudinal data with time dependent covariates we consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time the goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject however additional care must be taken to adjust for the association between the repeated measurements on each subject we propose a new maximum likelihood method for covariates that may be fixed or time varying we also implement and make comparisons with two other approaches generalized estimating equations which may be more robust to misspecification of the true correlation structure and alternating logistic regression which models association via odds ratios that are subject to less restrictive constraints than are correlations the proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter for equally spaced and complete data the gains in efficiency were greatest for the parameter associated with a time by group interaction term and for stronger values of the correlation for unequally spaced data and with dropout according to a missing at random mechanism mark1ml with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency we present an analysis to demonstrate application of the methods we consider we also offer an r function for easy implementation of our approach copyright 2012 john wiley sons ltd

method for efficient shape parametrization of fluid membranes and vesicles in this paper we describe a method for the parametrization of the shapes adopted by fluid membranes and vesicles the method is based upon a boundary value approach to geometry description in which smooth surfaces are produced as the solution to an elliptic partial differential equations shape parameters are introduced through the boundary conditions which control the shape of the vesicle models in combination with a model for the surface energy and a method for numerical minimization it is shown how the method can accurately approximate the shapes of both axisymmetric and nonaxisymmetric vesicles over a wide range of control parameters the particular value of the method lies in its ability to parametrize complicated shapes efficiently a feature that becomes especially valuable when seeking shapes of minimal energy using direct optimization techniques

a note on implementation of decaying product correlation structures for quasi least squares this note implements an unstructured decaying product matrix via the quasi least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations the structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix it is straightforward to show that the quasi least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure furthermore subject to conditions that are easily checked the quasi least squares estimators are valid for longitudinal bernoulli data we demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable

stochastic bifurcation in fitzhugh nagumo ensembles subjected to additive and or multiplicative noises abstract we have studied the dynamical properties of finite n unit fitzhugh nagumo fn ensembles subjected to additive and or multiplicative noises reformulating the augmented moment method amm with the fokker planck equation fpe method h hasegawa j phys soc japan 75 2006 033001 in the amm original 2 n dimensional stochastic equations are transformed to eight dimensional deterministic ones and the dynamics is described in terms of averages and fluctuations of local and global variables the stochastic bifurcation is discussed by a linear stability analysis of the deterministic amm equations the bifurcation transition diagram of multiplicative noise is rather different from that of additive noise the former has the wider oscillating region than the latter the synchronization in globally coupled fn ensembles is also investigated results of the amm are in good agreement with those of direct simulations dss

on the accuracy of efficiency of estimating equation approach summary liang and zeger 1986 biometrika73 13 22 introduced a generalized estimating equation gee approach based on a working correlation matrix to obtain efficient estimators of regression parameters in the class of generalized linear models for repeated measures data as demonstrated by crowder 1995 biometrika82 407 410 because of uncertainty of the definition of the working correlation matrix the liang zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters after taking this comment of crowder into account recently sutradhar and das 1999 biometrika86 459 465 examined the loss of efficiency of the regression estimators due to misspecification of the correlation structures but their study was confined to the regression estimation with cluster level covariates as in the original paper of liang and zeger in this paper we study this efficiency loss problem for the generalized regression models with within cluster covariates by utilizing the approach of sutsadhar and das 1999

mean field approximation for noisy delay coupled excitable neurons abstract mean field approximation of a large collection of fitzhugh nagumo excitable neurons with noise and all to all coupling with explicit time delays modelled by n 1 stochastic delay differential equations is derived the resulting approximation contains only two deterministic delay differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system

dynamical mean field theory of noisy spiking neuron ensembles application to the hodgkin huxley model a dynamical mean field approximation dma previously proposed by the present author h hasegawa phys rev e 67 041903 2003 has been extended to ensembles described by a general noisy spiking neuron model ensembles of n unit neurons each of which is expressed by coupled k dimensional differential equations des are assumed to be subject to spatially correlated white noises the original mathrm kn dimensional stochastic des have been replaced by k k 2 dimensional deterministic des expressed in terms of means and the second order moments of local and global variables the fourth order contributions are taken into account by the gaussian decoupling approximation our dma has been applied to an ensemble of hodgkin huxley hh neurons k 4 for which effects of the noise the coupling strength and the ensemble size on the response to a single spike input have been investigated numerical results calculated by the dma theory are in good agreement with those obtained by direct simulations although the former computation is about a thousand times faster than the latter for a typical hh neuron ensemble with n 100

analysis of repeated bouts of measurements in the framework of generalized estimating equations we consider a longitudinal study of interstitial cystitis ic in women in which the time between bouts of repeated measurements is large relative to the within bout separation in time our outcome of interest is the number of nocturnal voids that we model via quasi least squares qls in the framework of generalized estimating equations gee to account for potential intra subject correlation we directly apply a banded toeplitz correlation structure that previously was only implemented in an ad hoc approach using gee we describe this structure its appropriateness for data from the ic study and the results of our analysis we then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler structure can prevent substantial losses in efficiency in estimation of the regression parameter these comparisons involve the limiting values of the estimates of the correlation parameters which are not consistent for the misspecification scenarios considered here we therefore obtain the limiting values of the qls estimates when the structure is incorrectly specified

efficiency of generalized estimating equations for binary responses summary using standard correlation bounds we show that in generalized estimation equations gees the so called working correlation matrix r for analysing binary data cannot in general be the true correlation matrix of the data methods for estimating the correlation param eter in current gee software for binary responses disregard these bounds to show that the gee applied on binary data has high efficiency we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse fisher information matrix but r should be viewed as the weight matrix and it should not be confused with the correlation matrix of the binary responses we also do a comparison with more general weighted estimating equations by using a matrix cauchy schwarz inequality our analysis leads to simple rules for the choice of in an exchangeable or autoregressive ar 1 weight matrix r based on the strength of dependence between the binary variables an example is given to illustrate the assessment of dependence and choice of

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

modeling and computation of two phase geometric biomembranes using surface finite elements biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions the modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces this leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints in this paper we propose a new computational tool for computing equilibria based on an l 2 relaxation flow for the total energy in which the line energy is approximated by a surface ginzburg landau phase field functional the relaxation dynamics couple a nonlinear fourth order geometric evolution equation of willmore flow type for the membrane with a surface allen cahn equation describing the lateral decomposition a novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface the mean curvature vector and the surface phase field function the resulting variational formulation uses h 1 spaces and we employ triangulated surfaces and h 1 conforming quadratic surface finite elements for approximating solutions together with a semi implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells discocytes and starfishes with lateral phase separation

dynamical mean field theory of spiking neuron ensembles response to a single spike with independent noises a semianalytical dynamical mean field theory has been developed for a study of dynamics of an ensemble of n unit fitzhugh nagumo neurons subject to white noises assuming weak noises and the gaussian distribution of state variables we have driven equations of motions for moments of local and global variables dynamical mean field approximation dma has replaced original 2n dimensional stochastic differential equations des by eight dimensional deterministic des whereas the conventional moment method yields n 2n 3 dimensional deterministic des for local variables we have discussed the dependence of the spike firing precision and the synchronization on the noise intensity synaptic coupling and the size of the neuron ensemble the spike timing precision is shown to be improved by increasing the size of the neuron ensemble even when there are no couplings among neurons when the coupling is introduced neurons in ensembles respond to an input spike with a partial synchronization results calculated by our dma theory are in good agreement with those obtained by direct simulations dma theory is extended to a large cluster which can be divided into multiple subclusters according to their functions a model calculation has demonstrated that when the noise intensity is moderate the spike propagation with a fairly precise timing is possible among noisy subclusters with feed forward couplings as in the synfire chain we have compared dma theory with the conventional moment method showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean field approximation

simulating the deformation of vesicle membranes under elastic bending energy in three dimensions in this paper we study the three dimensional deformation of a vesicle membrane under the elastic bending energy with prescribed bulk volume and surface area both static and dynamic deformations are considered a newly developed energetic variational formulation is employed to give an effective eulerian description efficient time and spatial discretizations are considered and implemented numerical experiments illustrate some fascinating phenomena that are of interests in real applications

effects of distribution of infection rate on epidemic models a goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics however often the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics this discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models we show that when variability in infection rates is included in standard susciptible infected susceptible sis and susceptible infected recovered sir models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics this discrepancy holds for sis and sir models where the assumption that all individuals have the same sensitivity is eliminated in contrast with network models fixed partnerships are not assumed we derive a moment closure scheme capturing the distribution of sensitivities we find that the shape of the sensitivity distribution does not affect r 0 or the number of infected individuals in the early phases of the epidemics however a wide distribution of sensitivities reduces the total number of removed individuals in the sir model and the steady state infected fraction in the sis model the difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics the rate of change in the average infectivity should be computed these results are supported by a comparison of the theoretical model to the ebola epidemics and by numerical simulation

dynamics and absorption properties of stochastic equations with holder diffusion coefficients abstract in this article we characterize the dynamics and absorption properties of a class of stochastic differential equations around singular points where both the drift and diffusion functions vanish according to the holder coefficient of the diffusion function around the singular point we identify different regimes a regime where the solutions almost surely reach the singular point in finite time and regimes of exponential attraction or repulsion from the singular point stability of the absorbing state large deviations for the absorption time existence of stationary or quasi stationary distributions are discussed in particular we show that quasi stationary distributions only exist for 3 4 and for 3 4 1 no quasi stationary distribution is found and numerical simulations tend to show that the process conditioned on not being absorbed initiates an almost sure exponential convergence towards the absorbing state as is demonstrated to be true for 1 these results have several implications in the understanding of stochastic bifurcations and we completely unfold two generic situations the pitchfork and saddle node bifurcations and discuss the hopf bifurcation in the appendix

a finite element method to compute three dimensional equilibrium configurations of fluid membranes we introduce a finite element method to compute equilibrium configurations of fluid membranes identified as stationary points of a curvature dependent bending energy functional under certain geometric constraints the reparameterization symmetries in the problem pose a challenge in designing parametric finite element methods and existing methods commonly resort to lagrange multipliers or penalty parameters in contrast we exploit these symmetries by representing solution surfaces as normal offsets of given reference surfaces and entirely bypass the need for artificial constraints we then resort to a galerkin finite element method to compute discrete c 1 approximations of the normal offset coordinate the variational framework presented is suitable for computing deformations of three dimensional membranes subject to a broad range of external interactions we provide a systematic algorithm for computing large deformations wherein solutions at subsequent load steps are identified as perturbations of previously computed ones we discuss the numerical implementation of the method in detail and demonstrate its optimal convergence properties using examples we discuss applications of the method to studying adhesive interactions of fluid membranes with rigid substrates and to investigate the influence of membrane tension in tether formation

numerical observation of nonaxisymmetric vesicles in fluid membranes by means of surface evolver a software package of brute force energy minimization over a triangulated surface developed by the geometry center of the university of minnesota exp math 1 141 1992 we have numerically searched the nonaxisymmetric shapes under the helfrich spontaneous curvature sc energy model we show that there are abundant mechanically stable nonaxisymmetric vesicles in the sc model including both regular shapes with intrinsic geometric symmetry and complex irregular ones we report in this paper a catalog of interesting shapes including a corniculate shape with six corns a quadriconcave shape a shape resembling sickle cells a shape resembling acanthocytes and two tubelike shapes most of these shapes can be related to experimental observations in red blood cells and other experiments in fluid membrane s1063 651x 98 06510 6

augmented moment method for stochastic ensembles with delayed couplings ii fitzhugh nagumo model dynamics of fitzhugh nagumo fn neuron ensembles with time delayed couplings subject to white noises has been studied by using both direct simulations and a semianalytical augmented moment method amm which has been proposed in a preceding paper h hasegawa phys rev e 70 021911 2004 for n unit fn neuron ensembles amm transforms original 2n dimensional stochastic delay differential equations sddes to infinite dimensional deterministic des for means and correlation functions of local and global variables infinite order recursive des are terminated at the finite level m in the level m amm mathrm amm m yielding 8 m 1 dimensional deterministic des when a single spike is applied the oscillation may be induced if parameters of coupling strength delay noise intensity and or ensemble size are appropriate effects of these parameters on the emergence of the oscillation and on the synchronization in fn neuron ensembles have been studied the synchronization shows the fluctuation induced enhancement at the transition between nonoscillating and oscillating states results calculated by amm5 are in fairly good agreement with those obtained by direct simulations

approximate solution to the stochastic kuramoto model we study kuramoto phase oscillators with temporal fluctuations in the frequencies the infinite dimensional system can be reduced in a gaussian approximation to two first order differential equations this yields a solution for the time dependent order parameter which characterizes the synchronization between the oscillators the known critical coupling strength is exactly recovered by the gaussian theory extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value we obtain the asymptotic order parameter in closed form which suggests a tighter upper bound for the corresponding scaling as a last point we elaborate the gaussian approximation in complex networks with distributed degrees

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

sample size for a two group comparison of repeated binary measurements using gee controlled clinical trials often randomize subjects to two treatment groups and repeatedly evaluate them at baseline and intervals across a treatment period of fixed duration a popular primary objective in these trials is to compare the change rates in the repeated measurements between treatment groups repeated measurements usually involve missing data and a serial correlation within each subject the generalized estimating equation gee method has been widely used to fit the time trend in repeated measurements because of its robustness to random missing and misspecification of the true correlation structure in this paper we propose a closed form sample size formula for comparing the change rates of binary repeated measurements using gee for a two group comparison the sample size formula is derived incorporating missing patterns such as independent missing and monotone missing and correlation structures such as ar 1 model we also propose an algorithm to generate correlated binary data with arbitrary marginal means and a markov dependency and use it in simulation studies copyright 2005 john wiley sons ltd

augmented moment method for stochastic ensembles with delayed couplings i langevin model by employing a semianalytical dynamical mean field approximation theory previously proposed by the author h hasegawa phys rev e 67 041903 2003 we have developed an augmented moment method amm in order to discuss dynamics of an n unit ensemble described by langevin equations with delays in an amm original n dimensional stochastic delay differential equations sddes are transformed to infinite dimensional deterministic des for means and correlations of local as well as global variables infinite order des arising from the non markovian property of sdde are terminated at the finite level m in the level m amm mathrm amm m which yields 3 m dimensional deterministic des model calculations have been made for linear and nonlinear langevin models the stationary solution of amm for the linear langevin model with n 1 is nicely compared to the exact result in the nonlinear langevin ensemble the synchronization is shown to be enhanced near the transition point between the oscillating and nonoscillating states results calculated by amm6 are in good agreement with those obtained by direct simulations

effects of colored noise and noise delay on a calcium oscillation system abstract as a calcium oscillations system is in steady state the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods the results indicate that 1 the colored noise can induce coherence bi resonance phenomenon 2 there exist three peaks in the r 0 r is the reciprocal coefficient of variance and 0 is the self correlation time of the colored noise curves for the same noise intensity q 1 the gaussian colored noise can induce calcium spikes but the white noise cannot do this 3 the delay time can improve noise induced spikes regularity as 0 is small and r has a significant minimum with increasing as 0 is large 4 large values of reduce noise induced spikes regularity

the design of simulation studies in medical statistics by andrea burton douglas g altman patrick royston and roger l holder statistics in medicine 2006 25 4279 4292

determination of firing times for the stochastic fitzhugh nagumo neuronal model we present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models we apply the theory of first exit times for markov processes to the fitzhugh nagumo system with a constant mean gaussian white noise input representing stochastic excitation and inhibition partial differential equations are obtained for the moments of the time to first spike the observation that the recovery variable barely changes in the prespike trajectory leads to an accurate one dimensional approximation for the moments of the time to reach threshold this leads to ordinary differential equations that may be easily solved several analytical approaches are explored that involve perturbation expansions for large and small values of the noise parameter for ranges of the parameters appropriate for these asymptotic methods the perturbation solutions are used to establish the validity of the one dimensional approximation for both small and large values of the noise parameter additional verification is obtained with the excellent agreement between the mean and variance of the firing time found by numerical solution of the differential equations for the one dimensional approximation and those obtained by simulation of the solutions of the model stochastic differential equations such agreement extends to intermediate values of the noise parameter for the mean time to threshold we find maxima at small noise values that constitute a form of stochastic resonance we also investigate the dependence of the mean firing time on the initial values of the voltage and recovery variables when the input current has zero mean

structural stability for the morris lecar neuron model this paper is concerned with the biological neuron model of morris lecar system of equations morris and lecar 1981 17 we prove the existence and uniqueness of strong solutions in addition we prove the continuous dependence of solutions to the leak conductance parameter

correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria the method of generalized estimating equations gee is popular in the biostatistics literature for analyzing longitudinal binary and count data it assumes a generalized linear model for the outcome variable and a working correlation among repeated measurements in this paper we introduce a viable competitor the weighted scores method for generalized linear model margins we weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model because the weighted scores method is a parametric method based on likelihood we propose composite likelihood information criteria as an intermediate step for model selection the same criteria can be used for both correlation structure and variable selection simulations studies and the application example show that our method outperforms other existing model selection methods in gee from the example it can be seen that our methods not only improve on gee in terms of interpretability and efficiency but also can change the inferential conclusions with respect to gee copyright 2016 john wiley sons ltd

sample size calculations for studies with correlated observations correlated data occur frequently in biomedical research examples include longitudinal studies family studies and ophthalmologic studies in this paper we present a method to compute sample sizes and statistical powers for studies involving correlated observations this is a multivariate extension of the work by self and mauritsen 1988 biometrics 44 79 86 who derived a sample size and power formula for generalized linear models based on the score statistic for correlated data we appeal to a statistic based on the generalized estimating equation method liang and zeger 1986 biometrika 73 13 22 we highlight the additional assumptions needed to deal with correlated data some special cases that are commonly seen in practice are discussed followed by simulation studies

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

a generalized estimating equations approach for spatially correlated binary data applications to the analysis of neuroimaging data this paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects this approach is useful when the scientific focus is on modeling the marginal mean structure proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed the use of semivariogram models for parameterizing the correlation structure is discussed and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation the methodology is illustrated with neuroimaging data collected as part of the national institute of neurological disorders and stroke ninds stroke data bank a simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies

a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows we extend shravan k veerapaneni denis gueyffier denis zorin george biros a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d journal of computational physics 228 7 2009 2334 2353 to the case of three dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows although the main components of the algorithm are similar in spirit to the 2d case spectral approximation in space semi implicit time stepping scheme the main differences are that the bending and viscous force require new analysis the linearization for the semi implicit schemes must be rederived a fully implicit scheme must be used for the toroidal topology to eliminate a cfl type restriction and a novel numerical scheme for the evaluation of the 3d stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations by introducing these novel components we obtain a time scheme that experimentally is unconditionally stable has low cost per time step and is third order accurate in time we present numerical results to analyze the cost and convergence rates of the scheme to verify the solver we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid to illustrate the applicability of method we consider a few vesicle flow interaction problems the sedimentation of a vesicle interactions of one and three vesicles with a background poiseuille flow

improving the correlation structure selection approach for generalized estimating equations and balanced longitudinal data generalized estimating equations are commonly used to analyze correlated data choosing an appropriate working correlation structure for the data is important as the efficiency of generalized estimating equations depends on how closely this structure approximates the true structure therefore most studies have proposed multiple criteria to select the working correlation structure although some of these criteria have neither been compared nor extensively studied to ease the correlation selection process we propose a criterion that utilizes the trace of the empirical covariance matrix furthermore use of the unstructured working correlation can potentially improve estimation precision and therefore should be considered when data arise from a balanced longitudinal study however most previous studies have not allowed the unstructured working correlation to be selected as it estimates more nuisance correlation parameters than other structures such as ar 1 or exchangeable therefore we propose appropriate penalties for the selection criteria that can be imposed upon the unstructured working correlation via simulation in multiple scenarios and in application to a longitudinal study we show that the trace of the empirical covariance matrix works very well relative to existing criteria we further show that allowing criteria to select the unstructured working correlation when utilizing the penalties can substantially improve parameter estimation copyright 2014 john wiley sons ltd

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

dynamical mean field approximation to small world networks of spiking neurons from local to global and or from regular to random couplings by extending a dynamical mean field approximation previously proposed by the author h hasegawa phys rev e 67 041903 2003 we have developed a semianalytical theory which takes into account a wide range of couplings in a small world network our network consists of noisy n unit fitzhugh nagumo neurons with couplings whose average coordination number z may change from local z n to global couplings z n ensuremath 1 and or whose concentration of random couplings p is allowed to vary from regular p 0 to completely random p 1 we have taken into account three kinds of spatial correlations the on site correlation the correlation for a coupled pair and that for a pair without direct couplings the original 2n dimensional stochastic differential equations are transformed to 13 dimensional deterministic differential equations expressed in terms of means variances and covariances of state variables the synchronization ratio and the firing time precision for an applied single spike have been discussed as functions of z and p our calculations have shown that with increasing p the synchronization is worse because of increased heterogeneous couplings although the average network distance becomes shorter results calculated by our theory are in good agreement with those by direct simulations

approximate moment dynamics for chemically reacting systems in the stochastic formulation of chemical kinetics the differential equation that describes the time evolution of the lower order statistical moments for the number of molecules of the different species involved is generally not closed in the sense that the right hand side of this equation depends on higher order moments recent work has proposed a moment closure technique based on derivative matching which closes the moment equations by approximating higher order moments as nonlinear functions of lower order moments we here provide a mathematical proof of this moment closure technique and highlight its performance through comparisons with alternative methods these comparisons reveal that this moment closure technique based on derivative matching provides more accurate estimates of the moment dynamics especially when the population size is small finally we show that the accuracy of the proposed moment closure scheme can be arbitrarily increased by incurring additional computational effort

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a comparison of several approaches for choosing between working correlation structures in generalized estimating equation analysis of longitudinal binary data the method of generalized estimating equations gee models the association between the repeated observations on a subject with a patterned correlation matrix correct specification of the underlying structure is a potentially beneficial goal in terms of improving efficiency and enhancing scientific understanding we consider two sets of criteria that have previously been suggested respectively for selecting an appropriate working correlation structure and for ruling out a particular structure s in the gee analysis of longitudinal studies with binary outcomes the first selection criterion chooses the structure for which the model based and the sandwich based estimator of the covariance matrix of the regression parameter estimator are closest while the second selection criterion chooses the structure that minimizes the weighted error sum of squares the rule out criterion deselects structures for which the estimated correlation parameter violates standard constraints for binary data that depend on the marginal means in addition we remove structures from consideration if their estimated parameter values yield an estimated correlation structure that is not positive definite we investigate the performance of the two sets of criteria using both simulated and real data in the context of a longitudinal trial that compares two treatments for major depressive episode practical recommendations are also given on using these criteria to aid in the efficient selection of a working correlation structure in gee analysis of longitudinal binary data