on fractional order differential equations model for nonlocal epidemics a fractional order model for nonlocal epidemics is given stability of fractional order equations is studied the results are expected to be relevant to foot and mouth disease sars and avian flu

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

exact calculations for false discovery proportion with application to least favorable configurations in a context of multiple hypothesis testing we provide several new exact calculations related to the false discovery proportion fdp of step up and step down procedures for step up procedures we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable which leads to explicit computations of the c d f the s th moment and the mean of the fdp the latter corresponding to the false discovery rate fdr for step down procedures we derive what is to our knowledge the first explicit formula for the fdr valid for any alternative c d f of the p values we also derive explicit computations of the power for both step up and step down procedures these formulas are explicit in the sense that they only involve the parameters of the model and the c d f of the order statistics of i i d uniform variables the p values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true false hypotheses is used this new approach is used to investigate new results which are of interest in their own right related to least most favorable configurations for the fdr and the variance of the fdp

an adaptive step down procedure with proven fdr control under independence in this work we study an adaptive step down procedure for testing m hypotheses it stems from the repeated use of the false discovery rate controlling the linear step up procedure sometimes called bh and makes use of the critical constants iq m 1 i 1 q i 1 m motivated by its success as a model selection procedure as well as by its asymptotic optimality we are interested in its false discovery rate fdr controlling properties for a finite number of hypotheses we prove this step down procedure controls the fdr at level q for independent test statistics we then numerically compare it with two other procedures with proven fdr control under independence both in terms of power under independence and fdr control under positive dependence

pinning synchronization of fractional order delayed complex networks with non delayed and delayed couplings abstractthis paper considers the global synchronization of fractional order delayed complex networks with non delayed and delayed couplings based on pinning control with the help of comparison theorems for fractional order linear systems with multiple time delays some novel and useful synchronisation criteria are presented by adding linear error feedback controllers to certain selected nodes here the coupling matrices need not be symmetric or irreducible what is more it is shown that the model and results in the paper are more general than those in the literature a numerical example is given to demonstrate the effectiveness and feasibility of the obtained results

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

a bottom up approach to testing hypotheses that have a branching tree dependence structure with error rate control modern statistical analyses often involve testing large numbers of hypotheses in many situations these hypotheses may have an underlying tree structure that both helps determine the order that te

a note on adaptive bonferroni and holm procedures under dependence summary hochberg benjamini 1990 first presented adaptive procedures for controlling familywise error rate however until now it has not been proved that these procedures control the familywise error rate we introduce a simplified version of hochberg benjamini s adaptive bonferroni and holm procedures assuming a conditional dependence model we prove that the former procedure controls the familywise error rate in finite samples while the latter controls it approximately

bayes inference in regression models with arma p q errors we develop practical and exact methods of analyzing arma p 4 regression error models in a bayesian framework by using the gibbs sampling and metropolis hastings algorithms and we prove that the kernel of the proposed markov chain sampler converges to the true density the procedures can be applied to pure arma time series models and to determine features of the likelihood function by choosing appropriate diffuse priors our results are unconditional on the initial observations we also show how the algorithm can be further simplified for the important special cases of stationary ar p and invertible ma q models recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation examples with simulated and actual economic data are presented kpj ourls gibbs sampling metropolis hastings algorithm data augmentation time series arma processes markov chain bayesian statistics

generalized synchronization in complex dynamical networks via adaptive couplings abstract this paper investigates generalized synchronization of three typical classes of complex dynamical networks scale free networks small world networks and interpolating networks the proposed synchronization strategy is to adjust adaptively a node s coupling strength based on the node s local generalized synchronization information by taking the auxiliary system approach and using the lyapunov function method we prove that for any given initial coupling strengths the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems it is demonstrated that the coupling strengths are affected by topologies of the networks furthermore it is found that there are hierarchical features in the processes of generalized synchronization in scale free networks because of their highly heterogeneous distributions of connection degree finally we discuss in detail how a network s degree of heterogeneity affects its generalization synchronization behavior

strong control conservative point estimation and simultaneous conservative consistency of false discovery rates a unified approach summary the false discovery rate fdr is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses benjamini and hochberg introduced this quantity and proved that a particular step up p value method controls the fdr storey introduced a point estimate of the fdr for fixed significance regions the former approach conservatively controls the fdr at a fixed predetermined level and the latter provides a conservatively biased estimate of the fdr for a fixed predetermined significance region in this work we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent in particular the fdr point estimates can be used to define valid fdr controlling procedures in the asymptotic setting we also show that the point estimates can be used to estimate the fdr conservatively over all significance regions simultaneously which is equivalent to controlling the fdr at all levels simultaneously the main tool that we use is to translate existing fdr methods into procedures involving empirical processes this simplifies finite sample proofs provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence

consensus in a heterogeneous influence network we consider a dynamical network model in which a number of agents all move on the plane with the same constant absolute velocity at each time step each agent s direction is updated as the average of its direction plus the directions of other agents who can influence it the influencing capability of each agent is represented by its influencing radius which is randomly chosen according to a power law distribution with a scaling exponent between 2 and ensuremath infty as the value of the scaling exponent decreases the radius distribution becomes more heterogeneous and the network becomes much easier to achieve direction consensus among agents due to the leading roles played by a few hub agents furthermore almost all agents will finally move in the same desired direction in a strong heterogeneous influence network if and only if a small fraction of hub agents can be controlled to move in the desired direction these results also reflect the robust yet fragile feature of a heterogeneous influence network

novel adaptive strategies for synchronization of linearly coupled neural networks with reaction diffusion terms in this paper two types of linearly coupled neural networks with reaction diffusion terms are proposed we respectively investigate the adaptive synchronization of these two types of complex network models with local information of node dynamics some novel adaptive strategies to tune the coupling strengths among network nodes are designed by constructing appropriate lyapunov functionals and using inequality techniques several sufficient conditions are given for reaching synchronization by using the designed adaptive laws finally two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results

failure of parameter identification based on adaptive synchronization techniques in this paper several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so called adaptive synchronization techniques these failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit but also when this orbit is deliberately designed to be chaotic the reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved moreover synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally lipschitz in addition unknown parameter identification is studied in coupled systems with time delays

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

multiple testing in a two stage adaptive design with combination tests controlling fdr testing multiple null hypotheses in two stages to decide which of these can be rejected or accepted at the first stage and which should be followed up for further testing having had additional observations is of importance in many scientific studies we develop two procedures each with two different combination functions fisher s and simes to combine p values from two stages given prespecified boundaries on the first stage p values in terms of the false discovery rate fdr and controlling the overall fdr at a desired level the fdr control is proved when the pairs of first and second stage p values are independent and those corresponding to the null hypotheses are identically distributed as a pair p 1 p 2 satisfying the p clud property we did simulations to show that 1 our two stage procedures can have significant power improvements over the first stage benjamini hochberg bh procedure compared to the improvement offered by the ideal bh procedure that one would have used had the second stage

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

on the false discovery rate and an asymptotically optimal rejection curve in this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate fdr in multiple hypotheses testing problems we first give a heuristic motivation for this new curve and propose some procedures related to it then we introduce a set of possible assumptions and give a unifying short proof of fdr control for procedures based on simes critical values whereby certain types of dependency are allowed this methodology of proof is then applied to other fixed rejection curves including the proposed new curve among others we investigate the problem of finding least favorable parameter configurations such that the fdr becomes largest we then derive a series of results concerning asymptotic fdr control for procedures based on the new curve and discuss several example procedures in more detail a main result will be an asymptotic optimality statement for various procedures based on the new curve in the class of fixed rejection curves finally we briefly discuss strict fdr control for a finite number of hypotheses

dependency and false discovery rate asymptotics some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step up procedure lsu for testing n hypotheses when test statistics are dependent in this paper we investigate the expected error rate eer and the false discovery rate fdr in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses all results are derived in terms of p values in a general setup we present a series of results concerning the interrelation of simes rejection curve and the limiting empirical distribution function of the p values main objects under investigation are largest limiting crossing points between these functions which play a key role in deriving explicit formulas for eer and fdr as specific examples we investigate equi correlated normal and t variables in more detail and compute the limiting eer and fdr theoretically and numerically a surprising limit behavior occurs if these models tend to independence

structure identification of uncertain general complex dynamical networks with time delay it is well known that many real world complex networks have various uncertain information such as unknown or uncertain topological structure and node dynamics the structure identification problem has theoretical and practical importance for uncertain complex dynamical networks at the same time time delay often appears in the state variables or coupling coefficients of various practical complex networks this paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay in particular this method is also effective for uncertain delayed complex dynamical networks with different node dynamics moreover the proposed method can be easily extended to monitor the on line evolution of network topological structure finally three representative examples are then given to verify the effectiveness of the proposed approach

synchronization of fractional order complex dynamical networks abstract in this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied a fractional order controller for synchronization of complex network is presented some new sufficient synchronization criteria are proposed based on the lyapunov stability theory and the lasalle invariance principle these synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling configuration matrix and the inner coupling matrix are not assumed to be symmetric or irreducible it means that this method is more general and effective numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method

leader following consensus of fractional order multi agent systems via adaptive pinning control in this paper the leader following consensus problem of fractional order multi agent systems is considered via adaptive pinning control the dynamics of leader and all followers with linear and nonlinear functions are investigated respectively we assume that the node should be pinned if its in degree is less than its out degree in the paper under this assumption and based on the stability theory of fractional order differential systems some leader following consensus criteria are derived which are easily obtained by matrix inequalities the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented the design technique is based on algebraic graph theory and the riccati inequality several simulation examples are presented to demonstrate the effectiveness of the proposed method

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

adaptive and dynamic adaptive procedures for false discovery rate control and estimation summary many methods for estimation or control of the false discovery rate fdr can be improved by incorporating information about 0 the proportion of all tested null hypotheses that are true estimates of 0 are often based on the number of p values that exceed a threshold we first give a finite sample proof for conservative point estimation of the fdr when the parameter is fixed then we establish a condition under which a dynamic adaptive procedure whose parameter is determined by data will lead to conservative 0 and fdr estimators we also present asymptotic results on simultaneous conservative fdr estimation and control for a class of dynamic adaptive procedures simulation results show that a novel dynamic adaptive procedure achieves more power through smaller estimation errors for 0 under independence and mild dependence conditions we conclude by discussing the connection between estimation and control of the fdr and show that several recently developed fdr control procedures can be cast in a unifying framework where the strength of the procedures can be easily evaluated

exact filtering for partially observed continuous time models summary the forward backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods and which can be used to simulate from posterior distributions using a simple result which relates gamma random variables with different rates we show how the forward backward algorithm can be used to calculate the distribution of a sum of gamma random variables and to simulate from their joint distribution given their sum one application is to calculating the density of the time of a specific event in a markov process as this time is the sum of exponentially distributed interevent times this enables us to apply the forward backward algorithm to a range of new problems we demonstrate our method on three problems calculating likelihoods and simulating allele frequencies under a non neutral population genetic model analysing a stochastic epidemic model and simulating speciation times in phylogenetics

adaptive pinning cluster synchronization of fractional order complex dynamical networks the problem about cluster synchronization of fractional order cdns is studied via a pinning adaptive approach in this paper based on the stability theory of fractional differential equations some sufficient criteria for local and global cluster synchronization of fractional order cdns are derived in this paper the coupling configuration matrix can be asymmetric as well as reducible and the inner coupling matrix can also be asymmetric moreover the number of pinning nodes in each cluster can be evaluated especially when the coupling strength is large enough and the coupling configuration matrix is symmetric cluster synchronization can be achieved via pinning a single node in each cluster finally some typical examples are given to illustrate the correctness and effectiveness of our results a surprising finding is that the synchronization performance will become better as the fractional order decreases in this simulation

fractional pi pinning synchronization of fractional complex dynamical networks abstract a novel method for synchronization of fractional order complex dynamical networks using a new fractional proportional integral pi pinning control scheme is presented in this paper stability of this network is proved via the lyapunov stability theorem and the synchronizability criterion is obtained although one can also design a proportional pinning control scheme to synchronize the whole network our proposed fractional pi control is more efficient numerical simulations on lorenz oscillator s interaction over a sample network have shown that the proposed fractional pi controller can provide a faster synchronization with less overshoot to the reference state compared to conventional proportional controller with the same power consumption

chaos synchronization of general complex dynamical networks recently it has been demonstrated that many large scale complex dynamical networks display a collective synchronization motion here we introduce a time varying complex dynamical network model and further investigate its synchronization phenomenon based on this new complex network model two network chaos synchronization theorems are proved we show that the chaos synchronization of a time varying complex network is determined by means of the inner coupled link matrix the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network especially we do not assume that the coupled configuration matrix is symmetric and its off diagonal elements are nonnegative which in a way generalizes the related results existing in the literature

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

adaptive linear step up procedures that control the false discovery rate we provide a new two stage procedure in which the linear step up procedure is used in stage one to estimate mo providing a new level q which is used in the linear step up procedure in the second stage we prove that a general form of the two stage procedure controls the false discovery rate at the desired level q this framework enables us to study analytically the properties of other procedures that exist in the literature a simulation study is presented that shows that two stage adaptive procedures improve in power over the original procedure mainly because they provide tighter control of the false discovery rate we further study the performance of the current suggestions some variations of the procedures and previous suggestions in the case where the test statistics are positively dependent a case for which the original procedure controls the false discovery rate in the setting studied here the newly proposed two stage procedure is the only one that controls the false discovery rate the procedures are illustrated with two examples of biological importance

discovering the false discovery rate summary i describe the background for the paper controlling the false discovery rate a new and powerful approach to multiple comparisons by benjamini and hochberg that was published in the journal of the royal statistical society series b in 1995 i review the progress since made on the false discovery rate as well as the major conceptual developments that followed

adaptive pinning synchronization in fractional order uncertain complex dynamical networks with delay abstract based on the stability theory of fractional order systems synchronization of general fractional order uncertain complex networks with delay is investigated in this paper by the inequality of the fractional derivative and the comparison principle of the linear fractional equation with delay synchronization of complex networks with delay is realized under adaptive control some sufficient criteria ensuring local asymptotical synchronization under adaptive control and global asymptotical synchronization under adaptive pinning control are derived respectively finally numerical simulations are presented to demonstrate the validity and feasibility of the proposed synchronization criteria

some results on false discovery rate in stepwise multiple testing procedures the concept of false discovery rate fdr has been receiving increasing attention by researchers in multiple hypotheses testing this paper produces some theoretical results on the fdr in the context of stepwise multiple testing procedures with dependent test statistics it was recently shown by benjamini and yekutieli that the benjamini hochberg step up procedure controls the fdr when the test statistics are positively dependent in a certain sense this paper strengthens their work by showing that the critical values of that procedure can be used in a much more general stepwise procedure under similar positive dependency it is also shown that the fdr controlling benjamini liu step down procedure originally developed for independent test statistics works even when the test statistics are positively dependent in some sense an explicit expression for the fdr of a generalized stepwise procedure and an upper bound to the fdr of a step down procedure are obtained in terms of probability distributions of ordered components of dependent random variables before establishing the main results 1 introduction the main purpose of this paper is to present some formulas and inequalities providing theoretical insight into when and what stepwise procedures control the false discovery rate fdr at a prespecified level in multiple hypotheses testing the fdr first introduced in multiple testing by benjamini and hochberg 1995 is the expected proportion of erroneously rejected null hypotheses with v and r representing respectively the number of true null hypotheses rejected and the total number of null hypotheses rejected in a multiple testing procedure let q v r if r 0a nd 0i fr 0 then e q is the fdr of that procedure as they have argued it is an appropriate error rate to control in many practical situations particularly where a large number of null hypotheses are involved they also put forward an fdr controlling stepup procedure that is more powerful than comparable procedures controlling the traditional familywise error fwe rate when the underlying test statistics are independent benjamini and liu 1999 recently introduced a step down procedure with the same property the concept of fdr is now being used in a wide variety of applications abramovich and benjamini 1996 basford and tukey 1997 drigalenko

controllability of complex networks via pinning we study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy we define the pinning controllability of the network in terms of the spectral properties of an extended network topology the roles of the control and coupling gains as well as of the number of pinned nodes are also discussed

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

step up multiple testing of parameters with unequally correlated estimates we consider the problem of simultaneously testing k or to 2 hypotheses on parameters theta 1 theta k using test statistics t 1 t k such that a specified familywise error rate alpha is achieved dunnett and tamhane 1992a proposed a step up multiple test procedure in which testing starts with the hypothesis corresponding to the least significant test statistic and proceeds towards the most significant stopping the first time a significant test result is obtained and rejecting the hypotheses corresponding to that and any remaining test statistics the parameter estimates used in the t statistics were assumed to be normally distributed with a common variance which was a known multiple of an unknown sigma 2 and known correlations which were equal in the present article we show how the procedure can be extended to include unequally correlated parameter estimates unequal correlations occur for example in experiments involving comparisons among treatment groups with unequal sample sizes we also compare the step up and step down multiple testing approaches and discuss applications to some biopharmaceutical testing problems

analytical solution for post death transmission model of ebola epidemics abstract in this paper we shall introduce deceased human d transmission to the cycle phenomenon of disease modelling which has a direct relationship with the infective compartment of the stochastic susceptible infected recovered sir disease model due to this the noise covariance matrices of the standard stochastic sir model will be modified this will be done by using van kampen s expansion method to approximate the master equation and the stochastic fokker planck equation to analytically calculate a power spectral density psd expression a vector valued process is used and shows that the absolute value of the real part of the principal diagonal of the psd matrix solution is the spectral density of the system which is compared to the average psd of the stochastic simulations we aim to investigate the problem of identifiability when deceased humans act as an extended state of host infection using the sir d model during ebola epidemics using our analytical solution model we show that for an increasing degree of transmission parameter values the infected route cannot be identified whereas the deceased human transmission shows enhancement for the persistence of ebola virus disease using epidemiology data of the democratic republic of congo

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

adaptive false discovery rate control under independence and dependence in the context of multiple hypothesis testing the proportion 0 of true null hypotheses in the pool of hypotheses to test often plays a crucial role although it is generally unknown a priori a testing procedure using an implicit or explicit estimate of this quantity in order to improve its efficency is called adaptive in this paper we focus on the issue of false discovery rate fdr control and we present new adaptive multiple testing procedures with control of the fdr in a first part assuming independence of the p values we present two new procedures and give a unified review of other existing adaptive procedures that have provably controlled fdr we report extensive simulation results comparing these procedures and testing their robustness when the independence assumption is violated the new proposed procedures appear competitive with existing ones the overall best though is reported to be storey s estimator albeit for a specific parameter setting that does not appear to have been considered before in a second part we propose adaptive versions of step up procedures that have provably controlled fdr under positive dependence and unspecified dependence of the p values respectively in the latter case while simulations only show an improvement over non adaptive procedures in limited situations these are to our knowledge among the first theoretically founded adaptive multiple testing procedures that control the fdr when the p values are not independent

fast robust model selection in large datasets large datasets are increasingly common in many research fields in particular in the linear regression context it is often the case that a huge number of potential covariates are available to explain a response variable and the first step of a reasonable statistical analysis is to reduce the number of covariates this can be done in a forward selection procedure that includes selecting the variable to enter deciding to retain it or stop the selection and estimating the augmented model least squares plus t tests can be fast but the outcome of a forward selection might be suboptimal when there are outliers in this article we propose a complete algorithm for fast robust model selection including considerations for huge sample sizes because simply replacing the classical statistical criteria with robust ones is not computationally possible we develop simplified robust estimators selection criteria and testing procedures for linear regression the robust estimator is a one step weighted m estimato

novel algorithms to estimate nonlinear fdes applied to fractional order nutrient phytoplankton zooplankton system abstract in this paper dynamical behavior of a mathematical model for the interaction of nutrient phytoplankton and its predator zooplankton is investigated numerically stability analysis of the phytoplankton zooplankton model is studied by using the fractional routh hurwitz stability conditions we have studied the local stability of the equilibrium points then a new numerical algorithm as well as its modification for solving fractional differential equations fdes based on the polynomial interpolation is proposed the algorithms are designed to estimate linear and nonlinear fdes and they have the capability to apply for solving fractional order systems the convergence order and stability of the fractional higher order algorithms are proved and stability regions of the algorithms are achieved extensive numerical simulation results are provided and compared with the literature for illustrating the effectiveness and applicability of the presented algorithms to solve fractional differential equations the obtained analytical results are validated by numerical simulations and the global dynamics of the model system is studied

adaptive feedback control algorithm this paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers phys rev lett 93 214101 2004 phys rev e 71 037203 2005 69 067201 2004 where an adaptive feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems this note proves in detail the strictness of this algorithm from the viewpoint of mathematics and gives some interesting remarks for its potential applications to chaos control a synchronization in addition a significant comment on synchronization based parameter estimation is given which shows some techniques proposed in literature less strict and ineffective in some cases

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

statistical inference in a stochastic epidemic seir model with control intervention ebola as a case study a stochastic discrete time susceptible exposed infectious recovered seir model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of ebola in the democratic republic of congo in 1995 the incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach in order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions in addition a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions we develop markov chain monte carlo methods for inference that are used to explore the posterior distribution of the parameters the algorithm is further extended to integrate numerically over state variables of the model which are unobserved this provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments

adaptive pinning synchronization in fractional order complex dynamical networks abstract synchronization of general complex dynamical networks with fractional order dynamical nodes is addressed in this paper based on the stability theory of fractional order differential systems and adaptive pinning control some sufficient local asymptotical synchronization criteria and global asymptotical ones are derived respectively which succeed in solving the problem about how many nodes are need to be controlled and how much coupling strength should be applied to ensure the synchronization of the entire fractional order networks the obtained results are more general and effective than those reported moreover the coupling configuration matrices and the inner coupling matrices are not assumed to be symmetric and irreducible finally a numerical simulation is presented to demonstrate the validity and feasibility of the proposed synchronization criteria

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved