robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials in clinical trials comparing two treatments ordinal scales of three four or five points are often used to assess severity both prior to and after treatment analysis of covariance is an attractive technique however the data clearly violate the normality assumption and in the presence of small samples and large sample theory may not apply the robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation subjects are randomized to one of two competing treatments and the pre treatment or baseline assessment is used as the covariate we compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t test on difference scores under the null hypothesis of no difference in adjusted treatment means we estimated actual significance levels by comparing observed test statistics to appropriate critical values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypotheses the model which assumes homogeneous slopes and the t test on difference scores were robust in the presence of three four and five point ordinal scales the hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small the model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated the t test on difference scores also produced good power in the presence of small samples

brief paper design of highly synchronizable and robust networks in this paper the design of highly synchronizable sparse and robust dynamical networks is addressed better synchronizability means faster synchronization of the oscillators sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes links golden spectral dynamical networks graphs are those for which the spectral spread the difference between the largest and smallest eigenvalues of the adjacency matrix is equal to the spectral gap the difference between the two largest eigenvalues of the adjacency matrix multiplied by the square of the golden ratio these networks display the property of small worldness are very homogeneous and have large isoperimetric expansion constant together with a very high synchronizability and robustness to failures of individual oscillators in particular the regular bipartite dynamical networks reported here by the first time have the best possible expansion and consequently are the most robust ones against node link failures or intentional attacks

an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

synchronizable nodes in networked systems synchronization appears in networked systems as a phenomenon of interacting nodes the notion of synchronizability describes the property that the nodes can be forced to a synchronous behaviour by an appropriate interconnection structure whereas in earlier papers synchronizability has been investigated in terms of both the properties of the nodes and of the interconnection topology this paper shows that for linear coupled systems synchronizability is a property of the node dynamics alone if the nodes do not satisfy the necessary and sufficient synchronizability condition derived no interaction structure can ensure a synchronous behaviour of the networked system on the other hand if this condition is satisfied several interconnection structures given in this paper ensure synchronism globally in the whole state space

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

synchronizability of complex networks recent interest in the study of networks associated with complex systems has led to a better understanding of the factors and parameters relating the topology of the associated networks with the dynamics of the systems and in particular their synchronization in this paper by using known and new results from spectral graph theory we characterize relevant factors which affect the synchronization of complex networks

an improved strength pareto evolutionary algorithm 2 with application to the optimization of distributed generations this paper presents an improved strength pareto evolutionary algorithm 2 ispea2 which introduces a penalty factor in objective function constraints uses adaptive crossover and a mutation operator in the evolutionary process and combines simulated annealing iterative process over spea2 the testing result of ispea2 by authoritative testing functions meets the requirement of petro optimum fronts the case study result shows that the proposed algorithm provides a rapid convergence in obtaining pareto optimal solutions during the calculation process of evolution based on the fuzzy set theory ispea2 is able to solve the multi objective problems in the ieee 33 bus system and its validity and practicality are demonstrated by the utilization on dg s economic dispatch and optimal operation in the field of power industry

exemplary data set sample size calculation for wilcoxon mann whitney tests zhao rahardja and qu consider sample size calculation for wilcoxon mann whitney wmw tests for data with ties and present a straightforward formula we observe that the exemplary data set approach usually applied in more complex situations has a close relationship to the zhao rahardja qu method for wmw sample size estimation and they are asymptotically equivalent therefore the exemplary data set approach can be used to easily obtain estimates similar to those that the closed formula gives we illustrate application of both methods for a wmw sample size estimation example and also extend the simulation study presented by zhao et al we find that the zhao rahardja qu formula and by extension the exemplary data set method can give estimates just as accurate as those obtained using either the kolassa approach via nquery advisor or the o brien castelloe approach via sas 9 2 proc power for 1 1 and 1 2 allocation ratios however the latter two methods can be more accurate for a ratio of 1 4 or 1 19 finally we note the general utility of the exemplary data set approach for sample size estimation even in other situations where closed form sample size formulae exist

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

a unified framework for the comparison of treatments with ordinal responses different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable in this paper we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses the latent variable model is built upon the location scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables including the proportional odds model the ordered probit type model and the proportional hazards model a flexible estimation procedure is proposed for the identification and estimation of the general latent variable model which allows for the location and scale parameters to be freely estimated the framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data thus allowing for important statistical inferences such as location and or dispersion comparisons among treatments to be conveniently drawn analysis on real data sets is used to illustrate the proposed methods

brief paper synchronization of coupled harmonic oscillators in a dynamic proximity network in this paper we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity we show that the coupled harmonic oscillators can always be synchronized without imposing any network connectivity assumption moreover we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader again without any assumption on connectivity of the followers numerical simulation illustrates the theoretical results

analysis of matched case control data with multiple ordered disease states possible choices and comparisons in an individually matched case control study effects of potential risk factors are ascertained through conditional logistic regression clr extension of clr to situations with multiple disease or reference categories has been made through polychotomous clr and is shown to be more efficient than carrying out separate clrs for each subgroup in this paper we consider matched case control studies where there is one control group but there are multiple disease states with a natural ordering among themselves this scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease for example according to different stages of cancer we explore several popular models for ordered categorical data in this context we first adopt a cumulative logit or equivalently a proportional odds model to account for the ordinal nature of the data the important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum specific nuisance parameters cannot be eliminated in this model via the conditional likelihood approach we discuss a mantel haenszel approach for analysing such data we point out possible difficulties with standard likelihood based approaches with the cumulative logit model when applied to case control data we then consider an alternative conditional adjacent category logit model we illustrate the methods by analysing data from a matched case control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control a simulation study compares the different ordinal methods with methods ignoring sub classification of the ordered disease states

step up testing procedure for multiple comparisons with a control for a latent variable model with ordered categorical responses in clinical studies multiple comparisons of several treatments to a control with ordered categorical responses are often encountered a popular statistical approach to analyzing the data is to use the logistic regression model with the proportional odds assumption as discussed in several recent research papers if the proportional odds assumption fails to hold the undesirable consequence of an inflated familywise type i error rate may affect the validity of the clinical findings to remedy the problem a more flexible approach that uses the latent normal model with single step and stepwise testing procedures has been recently proposed in this paper we introduce a step up procedure that uses the correlation structure of test statistics under the latent normal model a simulation study demonstrates the superiority of the proposed procedure to all existing testing procedures based on the proposed step up procedure we derive an algorithm that enables the determination of the total sample size and the sample size allocation scheme with a pre determined level of test power before the onset of a clinical trial a clinical example is presented to illustrate our proposed method

complex network synchronizability analysis and control in this paper the investigation is first motivated by showing two examples of simple regular symmetrical graphs which have the same structural parameters such as average distance degree distribution and node betweenness centrality but have very different synchronizabilities for a given network with identical node dynamics it is further shown that two key factors influencing the network synchronizability are the network inner linking matrix and the eigenvalues of the network topological matrix several examples are then provided to show that adding new edges to a network can either increase or decrease the network synchronizability in searching for conditions under which the network synchronizability may be increased by adding edges it is found that for networks with disconnected complementary graphs adding edges never decreases their synchronizability moreover it is found that an unbounded synchronized region is always easier to analyze than a bounded synchronized region therefore to effectively enhance the network synchronizability a design method is finally presented for the inner linking matrix of rank 1 such that the resultant network has an unbounded synchronized region for the case where the synchronous state is an equilibrium point of the network

three structural properties reflecting the synchronizability of complex networks during the process of adding links we find that the synchronizability of the classical barabasi albert ba scale free or watts strogatz ws small world networks can be statistically quantified by three essentially structural quantities of these networks i e the eccentricity variance of the degree distribution and clustering coefficients the results indicate that both the eccentricity and clustering coefficient are positively linearly correlated with synchronizability while the variance is negatively linearly correlated moreover the efficiency of some particular strategies of adding links to change the synchronizability is also investigated this information can be used to guide us to design corresponding strategies of structure evolving processes to manipulate the synchronizability of a given network

complete synchronisation of linear oscillator networks oscillators with individual natural frequencies are not synchronisable by diffusive couplings which are usually used for solving consensus and synchronisation problems this article proves that however such oscillators can be synchronised by dynamical couplings if and only if the interconnection network includes local dynamical units with integrator dynamics a necessary and sufficient synchronisation condition shows that oscillators with arbitrary positive parameters are synchronised by any coupling network that possesses a spanning tree and has sufficiently large coupling strength simulation results illustrate the results of this article

altering synchronizability by adding and deleting edges for scale free networks abstract in this paper we propose two methods for altering the synchronizability of scale free networks 1 adding edges between the max degree nodes and min degree nodes 2 deleting edges between the max degree nodes and max degree nodes after adding and deleting edges we find that the former adding process can weaken synchronizability while the latter deleting process can enhance it the two processes adding and deleting can preserve the scale free structure the study of the average clustering coefficient indicates that it is not the most closely correlated with the synchronizability among the topological features considered our work also suggests that there are some essential relations between the network synchronization and the dynamics of economic systems they can be used to deal with some problems in the real world such as relieving the economic crisis in addition the adding and deleting processes may have potential applications in modifying network structure in view of their low cost

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

calculation of power and sample size with bounded outcome scores the two sample wilcoxon rank sum test is the most popular non parametric test for the comparison of two samples when the underlying distributions are not normal although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic parametric assumptions are often made to determine the power of the test or the sample size we encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients it is shown that for power and sample size estimation it can be dangerous to apply the classical formulae routinely especially with outcome scores having a u shaped or a j shaped distribution as an example we have taken the barthel index a quality of life outcome measure in stroke patients further we have investigated alternative methods by means of monte carlo simulation the distributional characteristics of the estimated powers were compared our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non parametric method

a novel strategy of pareto optimal solution searching in multi objective particle swarm optimization mopso in multi objective particle swarm optimization mopso algorithms finding the global optimal particle gbest for each particle of the swarm from a set of non dominated solutions is very difficult yet an important problem for attaining convergence and diversity of solutions first a new pareto optimal solution searching algorithm for finding the gbest in mopso is introduced in this paper which can compromise global and local searching based on the process of evolution the algorithm is implemented and is compared with another algorithm which uses the sigma method for finding gbest on a set of well designed test functions finally the multi objective optimal regulation of cascade reservoirs is successfully solved by the proposed algorithm

clustering and the synchronization of oscillator networks by manipulating the clustering coefficient of a network without changing its degree distribution we examine the effect of clustering on the synchronization of phase oscillators on networks with poisson and scale free degree distributions for both types of networks increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies surprisingly in scale free networks clustering promotes the synchronization of the most connected nodes hubs even though it inhibits global synchronization as a result they show an additional advanced transition instead of a single synchronization threshold this cluster enhanced synchronization of hubs may be relevant to the brain that is scale free and highly clustered

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

the use of bootstrap methods for estimating sample size and analysing health related quality of life outcomes health related quality of life hrqol measures are increasingly used in trials as primary outcome measures investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes hrqol outcomes like the sf 36 are usual measured on an ordinal scale although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes the ordered categories reflect contiguous intervals along this continuum the ordinal scaling of hrqol measures means they tend to generate data that have discrete bounded and skewed distributions thus standard methods of analysis that assume normality and constant variance may not be appropriate for this reason conventional statistical advice would suggest non parametric methods be used to analyse hrqol data the bootstrap is one such computer intensive non parametric method for estimating sample sizes and analysing data we describe three methods of estimating sample sizes for two group cross sectional comparisons of hrqol outcomes we then compared the power of the three methods for a two group cross sectional study design using bootstrap simulation the results showed that under the location shift alternative hypothesis conventional methods of sample size estimation performed well particularly whitehead s method whitehead s method is recommended if the hrqol outcome has a limited number of discrete values 7 and or the expected proportion of cases at either of the bounds is high if a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate than conventional methods finally we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters in an example data set we then compared and contrasted the bootstrap with standard methods of analysing hrqol outcomes in the data set studied with the sf 36 outcome the use of the bootstrap for estimating sample sizes and analysing hrqol data produces results similar to conventional statistical methods these results suggest that bootstrap methods are not more appropriate for analysing hrqol outcome data than standard methods

stabilizing weighted complex networks real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper the v stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics which includes the unweighted network as a special case pinning control is suggested to stabilize such a coupled network the complicated stabilization problem is reduced to measuring the semi negative property of the characteristic matrix which embodies not only the network topology but also the node self dynamics and the control gains it is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix the smaller the second largest eigenvalue is the more the network is pinning controllable numerical simulations of two representative networks composed of non chaotic systems and chaotic systems respectively are shown for illustration and verification

structural and spectral properties of a family of deterministic recursive trees rigorous solutions as one of the most significant models the uniform recursive tree urt has found many applications in a variety of fields in this paper we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees durts that are deterministic versions of urt firstly from the perspective of complex networks we investigate analytically the main structural characteristics of durts and obtain the accurate solutions for these properties which include degree distribution average path length distribution of node betweenness and degree correlations then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for durts our research may shed light on a better understanding of the features for urt also the analytical methods used here are capable of being extended to many other deterministic networks making the precise computation of their properties especially the full spectrum characteristics possible

sample size formula for the proportional hazards regression model a formula is derived for determining the number of observations necessary to test the equality of two survival distributions when concomitant information is incorporated this formula should be useful in designing clinical trials with a heterogeneous patient population schoenfeld 1981 biometrika 68 316 319 derived the asymptotic power of a class of statistics used to test the equality of two survival distributions that result is extended to the case where concomitant information is available for each individual and where the proportional hazards model holds the loss of efficiency caused by ignoring concomitant variables is also computed

factors that predict better synchronizability on complex networks while shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network the suppressing tendency of the heterogeneity of the degree distribution even for shorter characteristic path length has also been reported to see this we investigate the effects of various factors such as the degree characteristic path length heterogeneity and betweenness centrality on synchronization and find a consistent trend between the synchronization and the betweenness centrality the betweenness centrality is thus proposed as a good indicator for synchronizability

a weighted local world evolving network model with aging nodes abstract in this paper the dynamical behaviors of a class of weighted local world evolving networks with aging nodes are investigated as the network grows each newly added node is connected to some existing nodes through strength age preferential attachment each time step the newly added node with randomly determined initial degree is connected to some existing nodes through a local strength age preferential attachment by using tools from stochastic analysis and continuous approximation it is theoretically proved that the strength distribution of the generated network has a power law form with exponent depending nontrivially on a decay factor 0 1 in addition the clustering coefficient correlation and small world properties of this class of networks are examined via simulations it is shown that clustering coefficient is a monotone decreasing function of the decay factor and the assortative degree correlation and small world properties appear simultaneously finally the new model is used to characterize the internet topology as a typical application

relations between average distance heterogeneity and network synchronizability abstract by using the random interchanging algorithm we investigate the relations between average distance standard deviation of degree distribution and synchronizability of complex networks we find that both increasing the average distance and magnifying the degree deviation will make the network synchronize harder only the combination of short average distance and small standard deviation of degree distribution ensures strong synchronizability some previous studies assert that the maximal betweenness is the right quantity to estimate network synchronizability the larger the maximal betweenness the poorer the network synchronizability here we address an interesting case which strongly suggests that the single quantity maximal betweenness may not give a comprehensive description of network synchronizability

pairwise comparisons with ordered categorical data clinical trials frequently involve pairwise comparisons of different treatments to evaluate their relative efficacy in this study we examine methods for conducting pairwise tests of treatments with ordered categorical responses a modified version of the wilcoxon mann whitney test based on a logistic regression model assuming proportional odds is a popular choice for comparing two treatments this paper discusses the extension of this test to pairwise comparisons involving more than two treatments however when the proportional odds assumption is not valid the wilcoxon mann whitney type test procedure cannot control the overall type i error rate at the prespecified level of significance we therefore propose a better strategy in which a latent normal model is employed we presented a simulated comparative study of power and the overall type i error rate to illustrate the superiority of the latent normal model examples are also given for illustrative purposes copyright 2013 john wiley sons ltd

spectral reconstruction of complex networks abstract in this paper we study the reconstruction of a network topology from the eigenvalues of its laplacian matrix we introduce a simple cost function and consider the tabu search combinatorial optimization method while comparing its performance when reconstructing different categories of networks random regular small world scale free and clustered from their eigenvalues we show that this combinatorial optimization method together with the information contained in the laplacian spectrum allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders we also show that the method can be used to generate a quasi optimal topology for a network associated to a dynamic process like in the case of metabolic or protein protein interaction networks of organisms

spectral bounds for the betweenness of a graph in this paper we find spectral bounds laplacian matrix for the vertex and the edge betweenness of a graph we also relate the edge betweenness with the isoperimetric number and the edge forwarding and edge expansion indices of the graph allowing a new upper bound on its diameter the results are of interest as they can be used in the study of communication properties of real networks in particular for dynamical processes taking place on them broadcasting network synchronization virus spreading etc

a bayesian decision approach for sample size determination in phase ii trials stallard 1998 biometrics 54 279 294 recently used bayesian decision theory for sample size determination in phase ii trials his design maximizes the expected financial gains in the development of a new treatment however it results in a very high probability 0 65 of recommending an ineffective treatment for phase iii testing on the other hand the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error thall and simon 1994 biometrics 50 337 349 stallard s design maximizes the expected gain per phase ii trial but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion of treatments forwarding to the phase iii study we suggest maximizing the rate of gain and the resulting optimal one stage design becomes twice as efficient as stallard s one stage design furthermore the new design has a probability of only 0 12 of passing an ineffective treatment to phase iii study

sample size calculation for the wilcoxon mann whitney test adjusting for ties in this paper we study sample size calculation methods for the asymptotic wilcoxon mann whitney test for data with or without ties the existing methods are applicable either to data with ties or to data without ties but not to both cases while the existing methods developed for data without ties perform well the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties we propose a new method which has a closed form formula and therefore is very easy to calculate in addition the new method can be applied to both data with or without ties simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers

size and power estimation for the wilcoxon mann whitney test for ordered categorical data we derive an exact variance method for the size and power calculation for the wilcoxon mann whitney test for ordered categorical data the o brien castelloe approximation implemented in sas version 9 2 sas institute inc cary nc usa is simplified simulation studies show that the exact variance approach tends to be more accurate than the o brien castelloe approximation and the zhao rahardja qu method derived under local alternatives copyright 2011 john wiley sons ltd

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

choosing effective controlled nodes for scale free network synchronization abstract previous studies concerning pinning control of complex network synchronization have very often demonstrated that in an unweighted symmetrical scale free network controlling the high degree nodes is more efficient than controlling randomly chosen ones due to the heterogeneity of the node degree or edge connection distribution of the scale free network small degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network this raises the question of whether or not controlling the high degree nodes is always better than controlling the small ones in scale free networks our answer to this is yes and no in this study we carry out extensive numerical simulations to show that in an unweighted symmetrical barabasi albert scale free network when the portion of controlled nodes is relatively large controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones however we also show that for normalized weighted scale free networks controlling the big nodes is in fact always better than controlling the small ones

short term scheduling of cascade reservoirs using an immune algorithm based particle swarm optimization this paper presents a new approach for short term hydropower scheduling of reservoirs using an immune algorithm based particle swarm optimization ia pso ia pso is employed by coupling the immune information processing mechanism with the particle swarm optimization algorithm in order to achieve a better global solution with less computational effort with the ia pso technique the hydro electrical optimization model of reservoirs is formulated as a high dimensional dynamic nonlinear and stochastic global optimization problem of a multi reservoir hydropower system the purpose of the proposed methodology is to maximize total hydropower production here it is applied to a reservoir system on the qingjiang river in the yangtze watershed that consists of two reservoirs the results are compared with the results obtained through conventional operation method the dynamic programming and the standard pso algorithm from the comparative results it is found that the ia pso approach provides the most globally optimum solution at a faster convergence speed

a comparison of size and power calculations for the wilcoxon statistic for ordered categorical data this paper compares the accuracy of approximations to test size and power based on the score and the fisher information with calculations using edgeworth and cornish fisher approximations and demonstrates that in some cases one must exercise much care in using the simpler approximations

sample size calculations for studies with correlated ordinal outcomes correlated ordinal response data often arise in public health studies sample size power calculations are a crucial step in designing such studies to ensure an adequate sample to detect a significant effect here we extend rochon s method of sample size estimation with a repeated binary response to the ordinal case the proposed sample size calculations are based on an analysis with generalized estimating equations gee and inference with the wald test simulation results demonstrate the merit of the proposed power calculations analysis of an arthritis clinical trial is used for illustration

optimal sample size planning for the wilcoxon mann whitney test there are many different proposed procedures for sample size planning for the wilcoxon mann whitney test at given type i and type ii error rates and respectively most methods assume very specific models or types of data to simplify calculations eg ordered categorical or metric data location shift alternatives etc we present a unified approach that covers metric data with and without ties count data ordered categorical data and even dichotomous data for that we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following synthetic data approach we evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities then well known relations for the ranks of the data are used for the calculations in addition to computing the necessary sample size n for a fixed allocation proportion t n1 n where n1 is the sample size in the first group and n n1 n2 is the total sample size we provide an interval for the optimal allocation rate t which minimizes the total sample size n it turns out that for certain distributions a balanced design is optimal we give a characterization of such distributions furthermore we show that the optimal choice of t depends on the ratio of the two variances which determine the variance of the wilcoxon mann whitney statistic under the alternative this is different from an optimal sample size allocation in case of the normal distribution model

a practical approach to computing power for generalized linear models with nominal count or ordinal responses data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models many current proposals for dealing with binary ordinal or count outcomes are conceptually or computationally demanding limited in terms of accommodating covariates and or have not been extensively assessed for accuracy assuming moderate sample sizes here we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non continuous outcome the model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters the variance covariance matrix resulting from this fit is then used in conjunction with an established non central chi square approximation to the distribution of the wald statistic alternatively the model can be re fit under the null hypothesis to approximate power based on the likelihood ratio statistic we provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates relative to prior proposals the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing we illustrate the method for a variety of outcome types and covariate patterns using simulations to demonstrate its accuracy for realistic sample sizes

comparison of two treatments with skewed ordinal responses in clinical studies the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered however this model has been shown to be inappropriate when the proportional odds assumption is invalid mainly because it is unable to control the type i error rate in such circumstances to remedy this problem the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model however the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances when the underlying distributions are very different in skewness both of the aforementioned procedures suffer from the undesirable inflation of the type i error rate to solve the problem for clinical studies with ordinal responses we provide a viable solution that relies on the use of the latent weibull distribution which is a member of the log location scale family the proposed model is able to control the type i error rate regardless of the degree of skewness of the treatment responses in addition the power of the test also outperforms that of the latent normal model the testing procedure draws on newly developed theoretical results related to latent distributions from the location scale family the testing procedure is illustrated with two clinical examples