anova under unequal error variances by taking a generalized approach to findingp values the classical f test of the one way anova is extended to the case of unequal error variances the relationship of this result to other solutions in the literature is discussed an exact test for comparing variances of a number of populations is also developed scheff6 s procedure of multiple comparison is extended to the case of unequal variances the possibility and the approach that one can take to extend the results to simple designs involving more than one factor are briefly discussed

stationary consensus of heterogeneous multi agent systems with bounded communication delays consensus seeking is investigated for the discrete time heterogeneous multi agent systems composed of first order agents and second order agents and two stationary consensus algorithms are constructed for the first order agents and the second order agents respectively based on the properties of nonnegative matrices sufficient consensus criteria are obtained for the agents with bounded communication delays under fixed topology and switching topologies respectively with some prerequisites on the coupling weights and the sampling interval the asymptotic consensus achievement of the dynamic agents is independent of the communication delay but strictly depends on the connectedness of the interconnection topology simulation results illustrate the correctness of the results

passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

finite time consensus for controlled dynamical systems in network abstractthe key challenges in networked dynamical systems are the component heterogeneities nonlinearities and the high dimension of the formulated vector of state variables in this paper the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift for each model structure that defines homogeneous and heterogeneous multi system behaviour we derive protocols leading to finite time consensus for each model evolving in networks forming a homogeneous or heterogeneous multi system protocols integrating sufficient conditions are derived leading to finite time consensus likewise for the networking topology we make use of fixed directed and undirected graphs to prove our approaches finite time stability theory and lyapunov methods are considered as illustrative examples the homogeneous multi unicycle kinematics and the homogeneous heterogeneous multi second order dynamics in networks are studied

test for equality of intraclass correlation coefficients under unequal family sizes the likelihood ratio test the large sample z test and the large sample z test have been proposed to test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multinomial samples it has been found on the basis of simulation studies that the likelihood ratio test consistently and reliably produces results superior to those of the large sample z test and large sample z test in terms of power for various combinations of intraclass correlation coefficient values

a comparison of confidence interval methods for the intraclass correlation coefficient in cluster randomized trials a correction has been published for this article in statistics in medicine 23 18 2004 2935 this study compared different methods for assigning confidence intervals to the analysis of variance estimator of the intraclass correlation coefficient the context of the comparison was the use of to estimate the variance inflation factor when planning cluster randomized trials the methods were compared using monte carlo simulations of unbalanced clustered data and data from a cluster randomized trial of an intervention to improve the management of asthma in a general practice setting the coverage and precision of the intervals were compared for data with different numbers of clusters mean numbers of subjects per cluster and underlying values of the performance of the methods was also compared for data with normal and non normally distributed cluster specific effects results of the simulations showed that methods based upon the variance ratio statistic provided greater coverage levels than those based upon large sample approximations to the standard error of searle s method provided close to nominal coverage for data with normally distributed random effects adjusted versions of searle s method to allow for lack of balance in the data generally did not improve upon it either in terms of coverage or precision analyses of the trial data however showed that limits provided by thomas and hultquist s method may differ from those of the other variance ratio statistic methods when the arithmetic mean differs markedly from the harmonic mean cluster size the simulation results demonstrated that marked non normality in the cluster level random effects compromised the performance of all methods confidence intervals for the methods were generally wide relative to the underlying size of suggesting that there may be great uncertainty associated with sample size calculations for cluster trials where large clusters are randomized data from cluster based studies with sample sizes much larger than those typical of cluster randomized trials are required to estimate with a reasonable degree of precision copyright 2002 john wiley sons ltd

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

tests for individual and population bioequivalence based on generalized p values the u s food and drug administration fda has proposed new regulations that address the prescribability and switchability of new formulations of already approved drugs these new criteria are known respectively as population and individual bioequivalence two methods have been proposed in the bioequivalence literature for assessing population and individual bioequivalence that calculate an upper 95 per cent confidence bound for the bioequivalence criterion in question and then test bio equivalence by comparing this bound to the limit established by the fda in this paper we propose applying the generalized test function gtf methodology of tsui and weerahandi journal of the american statistical association 1989 602 607 to this problem to produce tests based on a generalized p value gpv this methodology allows us to construct hypothesis tests in the presence of nuisance parameters using simulation we show that these tests perform well in comparison to the confidence interval methods and have superior power for assessing population bioequivalence copyright 2003 john wiley sons ltd

testing reliability in a stress strength model when x and y are normally distributed we consider the stress strength problem in which a unit of strength x is subjected to environmental stress y an important problem in stress strength reliability concerns testing hypotheses about the reliability parameter r p x yl in this article we consider situations in which x and y are independent and have normal distributions or can be transformed to normality we do not require the two population variances to be equal our approach leads to test statistics which are exact p values that are represented as one dimensional integrals on the basis of the p value one can also construct approximate confidence intervals for the parameter of interest we also present an extension of the testing procedure to the case in which both strength and stress depend on covariates for comparative purposes the bayesian solution to the problem is also presented we use data from a rocket motor experiment to illustrate the procedure

exclusion process for particles of arbitrary extension hydrodynamic limit and algebraic properties the behaviour of extended particles with exclusion interaction on a one dimensional lattice is investigated the basic model is called l asep as a generalization of the asymmetric exclusion process asep to particles of arbitrary length l stationary and dynamical properties of the l asep with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many body system in particular the hydrodynamic equation for the local density evolution and the time dependent diffusion constant of a tracer particle are calculated as a fundamental algebraic property of the symmetric exclusion process the su 2 symmetry is generalized to the case of extended particles

consensus of heterogeneous multi agent systems without velocity measurements this article considers the consensus problem of heterogeneous multi agent system composed of first order and second order agents in which the second order integrator agents cannot obtain the velocity second state measurements for feedback two different consensus protocols are proposed first we propose a consensus protocol and discuss the consensus problem of heterogeneous multi agent system by applying the graph theory and the lyapunov direct method some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader following networks second due to actuator saturation we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi agent system finally some examples are presented to illustrate the effectiveness of the obtained criterions

a comparison of confidence interval methods for the intraclass correlation coefficient summary different methods of obtaining confidence intervals for the intraclass correlation coefficient p in the unbalanced one way random effects model are investigated focusing on applications to family studies methods based on simple modifications of formulas for the case of equal group sizes are found to provide adequate coverage at small to moderate values of p a method based on the large sample standard error of the sample intraclass correlation as derived by smith 1956 annals of human genetics 21 363 373 is shown to provide consistently good coverage at all values of p a method proposed by thomas and hultquist 1978 annals of statistics 6 582 587 also provides consistently good coverage but generates mean interval widths substantially greater than those generated by smith s method at values of p likely to arise in practice

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

group consensus control for heterogeneous multi agent systems with fixed and switching topologies abstractin this paper the group consensus problems of heterogeneous multi agent systems with fixed and switching topologies are investigated first a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi agent systems by using the neighbours information then some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus rigorous proofs are given by using graph theory matrix theory and lyapunov theory finally numerical simulations are also given to verify the theoretical analysis

necessary and sufficient conditions for consensus of double integrator multi agent systems with measurement noises an average consensus protocol is proposed for continuous time double integrator multi agent systems with measurement noises under fixed topologies the time varying control gain is employed to attenuate noises the closed loop system is therefore a time varying linear stochastic differential equation by determining the state transition matrix of this closed loop system the dynamic characteristics of the multi agent system can be fully described it is proved that in the noisy communication environment the average consensus can be achieved if and only if the communication topology is a balanced and strongly connected graph and the time varying control gain satisfies the stochastic approximation type conditions under the proposed protocol the position of each agent is convergent in mean square to a common random variable whose mathematical expectation is the average of initial positions and initial velocities of all agents in the system while each agent s velocity is convergent in mean square to a common random variable whose mathematical expectation and variance are both zero

exact inference for growth curves with intraclass correlation structure summary we consider repeated observations taken over time for each of several subjects for example one might consider the growth curve of a cohort of babies over time we assume a simple linear growth curve model exact results based on sufficient statistics exact tests of the null hypothesis that a coefficient is zero or exact confidence intervals for coefficients are not available to make inference on regression coefficients when an intraclass correlation structure is assumed this paper will demonstrate that such exact inference is possible using generalized inference

consensus tracking for higher order multi agent systems with switching directed topologies and occasionally missing control inputs abstract this paper studies the distributed consensus tracking problem of linear higher order multi agent systems with switching directed topologies and occasionally missing control inputs in this framework the underlying topology of dynamic agents may switch among several directed graphs each having a directed spanning tree rooted at the leader furthermore the control inputs to the followers may be temporally missed due to actuator failures and network induced packet loss to guarantee asymptotic consensus tracking in such a multi agent system several distributed controllers are constructed based only on the relative state information of neighboring agents by appropriately constructing a switching lyapunov function and using tools from the m matrix theory some sufficient conditions for achieving distributed consensus tracking are provided finally some numerical simulations are given to illustrate the theoretical analysis

non parametric bootstrap confidence intervals for the intraclass correlation coefficient the intraclass correlation coefficient rho plays a key role in the design of cluster randomized trials estimates of rho obtained from previous cluster trials and used to inform sample size calculation in planned trials may be imprecise due to the typically small numbers of clusters in such studies it may be useful to quantify this imprecision this study used simulation to compare different methods for assigning bootstrap confidence intervals to rho for continuous outcomes from a balanced design data were simulated for combinations of numbers of clusters 10 30 50 intraclass correlation coefficients 0 001 0 01 0 05 0 3 and outcome distributions normal non normal continuous the basic bootstrap t percentile bias corrected and bias corrected accelerated bootstrap intervals were compared with new methods using the basic and bootstrap t intervals applied to a variance stabilizing transformation of rho the standard bootstrap methods provided coverage levels for 95 per cent intervals that were markedly lower than the nominal level for data sets with only 10 clusters and only provided close to 95 per cent coverage when there were 50 clusters application of the bootstrap t method to the variance stabilizing transformation of rho improved upon the performance of the standard bootstrap methods providing close to nominal coverage

a matrix approach to graph maximum stable set and coloring problems with application to multi agent systems using the semi tensor product of matrices this paper investigates the maximum weight stable set and vertex coloring problems of graphs with application to the group consensus of multi agent systems and presents a number of new results and algorithms firstly by defining a characteristic logical vector and using the matrix expression of logical functions an algebraic description is obtained for the internally stable set problem based on which a new algorithm to find all the internally stable sets is established for any graph secondly the maximum weight stable set problem is considered and a necessary and sufficient condition is presented by which an algorithm to find all the maximum weight stable sets is obtained thirdly the vertex coloring problem is studied by using the semi tensor product method and two necessary and sufficient conditions are proposed for the colorability based on which a new algorithm to find all the k coloring schemes and minimum coloring partitions is put forward finally the obtained results are applied to multi agent systems and a new protocol design procedure is presented for the group consensus problem the study of illustrative examples shows that the results algorithms presented in this paper are very effective

statistical analysis of intraclass correlations from multiple samples with applications to arterial blood pressure data we consider inference procedures on intraclass correlations for unbalanced data from several multivariate normal populations we derive several tests including ones based on fisher s variance stabilizing transformation and neyman s score functions to test the homogeneity of intraclass correlations we illustrate the methodology with an example that uses arterial blood pressure data collected by miall and oldham and we compare the procedures in terms of their empirical levels and powers with a monte carlo simulation study we recommend the use of neyman s c alpha test and a test based on the anova estimators of the intraclass correlations as they hold their significance levels and give consistently higher powers

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

consensus seeking in multi agent systems with multiplicative measurement noises abstract in this paper the consensus problems of the continuous time integrator systems under noisy measurements are considered the measurement noises which appear when agents measure their neighbors states are modeled to be multiplicative by multiplication of the noises here the noise intensities are proportional to the absolute value of the relative states of an agent and its neighbor by using known distributed protocols for integrator agent systems the closed loop system is described in the vector form by a singular stochastic differential equation for the fixed and switching network topology cases constant consensus gains are properly selected such that mean square consensus and strong consensus can be achieved especially exponential mean square convergence of agents states to the common value is derived for the fixed topology case in addition asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied simulations shed light on the effectiveness of the proposed theoretical results

the spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton abstract we obtained the exact solution of a probabilistic cellular automaton related to the diagonal to diagonal transfer matrix of the six vertex model on a square lattice the model describes the flow of ants or particles traveling on a one dimensional lattice whose sites are small craters containing sleeping or awake ants two kinds of particles we found the bethe ansatz equations and the spectral gap for the time evolution operator of the cellular automaton from the spectral gap we show that in the asymmetric case it belongs to the kardar parisi zhang kpz universality class exhibiting a dynamical critical exponent value z 3 2 this result is also obtained from a direct monte carlo simulation by evaluating the lattice size dependence of the decay time to the stationary state

testing variance components in mixed models with generalized p values abstract a procedure for testing one sided hypotheses on variance components in a balanced random effects model is developed the testing is performed on the basis of a generalized p value and involves a one dimensional numerical integration in the special case for which the conventional methods provide an exact test this test is equivalent to the usual f test the test is also generalized bayes in the sense that under a certain diffuse prior the p value is numerically the same as the posterior probability of the null hypothesis

hard rod gas with long range interactions exact predictions for hydrodynamic properties of continuum systems from discrete models one dimensional hard rod gases are explicitly constructed as the limits of discrete systems exclusion processes involving particles of arbitrary length those continuum many body systems in general do not exhibit the same hydrodynamic properties as the underlying discrete models considering as examples a hard rod gas with additional long range interaction and the generalized asymmetric exclusion process for extended particles it is shown how a correspondence between continuous and discrete systems must be established instead this opens up a possibility to exactly predict the hydrodynamic behavior of this continuum system under eulerian scaling by solving its discrete counterpart with analytical or numerical tools as an illustration simulations of the totally asymmetric exclusion process are compared to analytical solutions of the model and applied to the corresponding hard rod gas the case of short range interaction is treated separately

a new approach for interval estimation and hypothesis testing of a certain intraclass correlation coefficient the generalized variable method we consider the problems of interval estimation and hypothesis testing for the intraclass correlation coefficient in an interrater reliability study when both raters and subjects are assumed to be randomly selected from populations of raters and subjects respectively we propose a novel approach for the confidence interval estimation and hypothesis testing using the concepts of generalized confidence interval gci and generalized p values a simulation study is conducted to investigate the coverage probabilities of the gci approach relative to the modified large sample mls approach both methods tend to provide somewhat conservative coverage relative to the mls approach the gci approach is closer to the correct nominal coverage for a two sided interval but farther to the correct coverage for a one sided lower interval unlike the mls approach the gci approach can also easily provide p values the fact that the gci approach is suitable for confidence interval estimation and obtaining p values makes the gci approach a suitable candidate for making inference about interrater reliability

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

consensus seeking over random weighted directed graphs we examine the consensus problem for a group of agents that communicate via a stochastic information network communication among agents is modeled as a weighted directed random graph that switches periodically the existence of any edge is probabilistic and independent from the existence of any other edge we further allow each edge to be weighted differently sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights

interval estimation and hypothesis testing of intraclass correlation coefficients the generalized variable approach in this paper we propose a novel approach using the concept of generalized variable gv for the confidence interval estimation of the difference of two intraclass correlation coefficients under unequal family sizes this approach can also easily provide p values for hypothesis testing simulation results show that the gv approach can provide confidence intervals with good coverage properties and perform hypothesis testing with satisfactory type i error control furthermore the confidence intervals and p values by gv approach can be easily obtained by simulation therefore the gv approach is a suitable candidate for making inference concerning two intraclass correlation coefficients

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem in these generalized models the range of the hard core interactions are changed and the restriction of relative ordering of the particles is partially broken the models probing these effects are those of biased diffusion of particles having size s 0 1 2 dots or an effective negative size s ensuremath 1 ensuremath 2 dots in units of lattice space our numerical simulations show that irrespective of the range of the hard core potential as long some relative ordering of particles are kept we find suitable sliding tag correlation functions whose fluctuations growth with time anomalously slow t 1 3 when compared with the normal diffusive behavior t 1 2 these results indicate that the critical behavior of these stochastic models are in the kardar parisi zhang kpz universality class moreover a previous bethe ansatz calculation of the dynamical critical exponent z for size sg 0 particles is extended to the case sl0 and the kpz result z frac 3 2 is predicted for all values of s ensuremath in z

some tests for variance components using generalized p values the concept of a generalized p value introduced by tsui and weerahandi is applied for testing hypotheses in two situations testing the significance of a variance component in a general balanced mixed model when an exact f test does not exist and comparing randomeffects variance components in two independent balanced mixed models extensions to the unbalanced cases are also indicated the proposed test is compared with the test based on the satterthwaite approximation through their simulated type i error probabilities the simulations indicate that the test based on the generalized p value hastype i error probabilities less than the chosen significance level most of the time whereas the type i error probabilities of the satterthwaite approximate test can be much larger than the significance level the results are illustrated using two examples