optimal designs of two phase studies the two phase design is a cost effective sampling strategy to evaluate the effects of covariates on an outcome when certain covariates are too expensive to be measured on all study subjects under

criteria for asymptotic stability of linear time delay systems several sufficient conditions which guarantee stability of linear time delay systems are derived each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

stability criteria of linear neutral systems with multiple delays in the present note stability of linear neutral systems with multiple delays is investigated by principle of the argument stability criteria are derived which are necessary and sufficient for asymptotic stability of the neutral systems the stability criteria need only to evaluate the characteristic function and the argument on the boundary of a certain rectangular region several numerical examples are given to illustrate the results

novel delay dependent kalman luenberger type filter design for neutral systems this article presents a new delay dependent condition to design a kalman luenberger type filter for neutral systems where the resulting filter is such that a prescribed level is guaranteed the proposed approach is based on linear matrix inequalities and on lyapunov krasovskii theory also the gu s discretisation method and a slack matrix technique that decouples the system matrices from the lyapunov ones are applied in order to obtain less conservative results than the similar ones two numerical examples are performed to illustrate the advantage of the method proposed

power calculation for case cohort studies with nonrare events summary case cohort design has been advocated in many epidemiologic studies when studying rare diseases or events in this design with a rare event all the events are selected for risk factor assessment when the event is not rare it is desirable to consider a generalized case cohort design where only a fraction of events are sampled we provide a valid test statistic to compare hazards functions between two samples for this generalized design and give a method for calculating power our result generalizes the result in cai and zeng 2004 biometrics60 1015 1024 and it shows numerically that efficiency loss due to sampling only part of the events is very low under nonrare events situation

more efficient estimators for case cohort studies the case cohort study design used to reduce costs in large cohort studies is a random sample of the entire cohort named the subcohort augmented with subjects having the disease of interest but not in the subcohort sample when several diseases are of interest several case cohort studies may be conducted using the same subcohort with each disease analyzed separately ignoring the additional exposure measurements collected on subjects with the other diseases this is not an efficient use of the data and in this paper we propose more efficient estimators we consider both joint and separate analyses for the multiple diseases we propose an estimating equation approach with a new weight function and we establish the consistency and asymptotic normality of the resulting estimator simulation studies show that the proposed methods using all available information gain efficiency we apply our proposed method to the data from the busselton health study

risk ratio and rate ratio estimation in case cohort designs hypertension and cardiovascular mortality multivariate analysis in case base designs depends on approximate methods in the present study new pseudo likelihood methods are developed for this design with these methods the case cohort risk ratio and rate ratio as well as their standard errors are easily estimated using logistic regression and poisson regression respectively this is illustrated by the association between hypertension and cardiovascular mortality in a cohort estimated by case cohort analysis using samples of several sizes the estimates are compared with those obtaining in full cohort and nested case control designs the results indicate that these methods which require nothing but widely available computer software are valid the case cohort design therefore is a good sometimes even advantageous alternative to the nested case control design in studying a disease that is not very rare application of the risk ratio method to the full cohort using a sample of 100 per cent follows logically whenever the true risk ratio is desired instead of the odds ratio a multivariate model for its estimation is therefore available

classes of degeneracy loci for quivers the thom polynomial point of view the chern classes for degeneracy loci of quivers are natural generalizations of the thom porteous giambelli formula suppose that e f are vector bundles over a manifold m and that s e f is a vector bundle homomorphism the question is which cohomology class is defined by the set6k s m consisting of points m where the linear map s m has corank k the answer due to i porteous is a determinant in terms of chern classes of the bundles e f we can generalize the question by giving more bundles over m and bundle maps among them the situation can be conveniently coded by an oriented graph called a quiver assigning vertices for bundles and arrows for maps we give a new method for calculating chern class formulae for degeneracy loci of quivers we show that for representation finite quivers this is a special case of the problem of calculating thom polynomials for group actions this allows us to apply a method for calculating thom polynomials developed by the authors the method reducing the calculations to solving a system of linear equations is quite different from the method of a buch and w fulton developed for calculating chern class formulae for degeneracy loci of a n quivers and it is more general can be applied to an dn e6 e7 and e8 quivers we provide sample calculations for a 3 and d4 quivers

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

a smooth space of tetrahedra abstract we construct a smooth symmetric compactification of the space of all labeled tetrahedra in p 3

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

new stability analysis for linear neutral system via state matrix decomposition this paper deals with the problem of delay dependent stability for neutral systems the matrix decomposition technique is employed to reduce the conservativeness of stability conditions the main results are extended to the neutral system with time varying uncertainties the proposed methods are with simpler form in terms of lmi and better performance than the existing ones in the literatures numerical examples are given to illustrate the effectiveness of the proposed methods

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

delay dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay this paper focuses on the delay dependent stability analysis and stabilization for fuzzy control systems with time delay based on linear matrix inequality lmi approach a delay dependent stability criteria has been developed the design schemes of stabilization via state feedback is developed and then the result is extended to the case of observer based output feedback all the researching results are presented by means of lmis two illustrative examples are given to illustrate the validity of the proposed design procedures

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

asymptotic stability of impulsive control neutral type systems in this paper we consider a delay control system of neutral type applying lyapunov functions and razumikhin technique combining with an impulsive feedback control we established some criteria for asymptotic stability of the system an example is also discussed to illustrate the main results we show that by means of appropriate impulsive perturbations we can control the stability behaviour of the system

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

the general quadruple point formula maps between manifolds m m to n m ell ell0 have multiple points and more generally multisingularities the closure of the set of points where the map has a particular multisingularity is called the multisingularity locus there are universal relations among the cohomology classes represented by multisingularity loci and the characteristic classes of the manifolds these relations include the celebrated thom polynomials of monosingularities for multisingularities however only the form of these relations is clear in general due to kazarian the concrete polynomials occurring in the relations are much less known in the present paper we prove the first general such relation outside the region of morin maps the general quadruple point formula we apply this formula in enumerative geometry by computing the number of 4 secant linear spaces to smooth projective varieties some other multisingularity formulas are also studied namely 5 6 7 tuple point formulas and one corresponding to sigma 2 sigma 0 multisingularities

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

on computing the maximum time delay bound for stability of linear neutral systems this note is concerned with the stability problem of linear delay differential systems of neutral type a discretized lyapunov functional approach is developed the resulting stability criterion is formulated in the form of a linear matrix inequality for nominal systems the analytical results can be approached with fine discretization numerical examples show significant improvement over approaches in the literature

thom polynomials symmetries and incidences of singularities as an application of the generalized pontryagin thom construction rsz here we introduce a new method to compute cohomological obstructions of removing singularities i e thom polynomials t with the aid of this method we compute some sample results such as the thom polynomials associated to all stable singularities of codimension 8 between equal dimensional manifolds and some other thom polynomials associated to singularities of maps n n p n k for k 0 we also give an application by reproving a weak form of the multiple point formulas of herbert and ronga h ro2 as a byproduct of the theory we define the incidence class of singularities which the author believes may turn to be an interesting useful and simple tool to study incidences of singularities

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

stability of linear neutral systems with multiple delays boundary criteria the stability of linear neutral delay differential systems with multiple delays is investigated the delay dependent stability criteria are presented through the evaluation of the corresponding harmonic functions on the boundary of a certain half circular region and such criteria are extensions of some results in literature an example is given to illustrate the stability criteria

marginal hazards model for case cohort studies with multiple disease outcomes case cohort study designs are widely used to reduce the cost of large cohort studies while achieving the same goals especially when the disease rate is low a key advantage of the case cohort study design is its capacity to use the same subcohort for several diseases or for several subtypes of disease in order to compare the effect of a risk factor on different types of diseases times to different events need to be modelled simultaneously valid statistical methods that take the correlations among the outcomes from the same subject into account need to be developed to this end we consider marginal proportional hazards regression models for case cohort studies with multiple disease outcomes we also consider generalized case cohort designs that do not require sampling all the cases which is more realistic for multiple disease outcomes we propose an estimating equation approach for parameter estimation with two different types of weights consistency and asymptotic normality of the proposed estimators are established large sample approximation works well in small samples in simulation studies the proposed methods are applied to the busselton health study

technical communique a new result on stability analysis for stochastic neutral systems this paper discusses the mean square exponential stability of stochastic linear systems of neutral type applying the lyapunov krasovskii theory a linear matrix inequality based delay dependent stability condition is presented the use of model transformations cross term bounding techniques or additional matrix variables is all avoided thus the method leads to a simple criterion and shows less conservatism the new result is derived based on the generalized finsler lemma gfl gfl reduces to the standard finsler lemma in the absence of stochastic perturbations and it can be used in the analysis and synthesis of stochastic delay systems moreover gfl is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results

selecting an efficient design for assessing exposure disease relationships in an assembled cohort summary we develop approximate methods to compare the efficiencies and to compute the power of alternative potential designs for sampling from a cohort before beginning to collect exposure data our methods require only that the cohort be assembled meaning that the numbers of individuals nkj at risk at pairs of event times tk and ti tk are available to compute nkj one needs to know the entry follow up censoring and event history but not the exposure for each individual our methods apply to any unbiased control sampling design in which cases are compared to a random sample of noncases at risk at the time of an event we apply our methods to approximate the efficiencies of the nested case control design the case cohort design and an augmented case cohort design compared to the full cohort design in an assembled cohort of 17 633 members of an insurance cooperative who were followed for mortality from prostatic cancer the assumptions underlying the approximation are that exposure is unrelated both to the hazard of an event and to the hazard for censoring the approximations performed well in simulations when both assumptions held and when the exposure was moderately related to censoring

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

stability of perturbed systems with time varying delays abstract this paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time delay systems subject to parametric unstructured or highly structured perturbations the criteria given in this paper are delay independent or delay dependent the considered delay may be time varying an estimation of the transient behaviour of the studied systems is also provided exponential rate of convergence scalar or vectorial inequalities involving hurwitz matrices matrix measures and norms constitute the mathematical foundations of the exposed results

lyapunov equation for the stability of linear delay systems of retarded and neutral type in this note the delay independent stability of delay systems is studied it is shown that the strong delay independent stability is equivalent to the feasibility of certain linear matrix inequality lmi that is to the existence of a quadratic lyapunov krasovskii functional independent of the nonnegative value of the delay this constitutes the analogue of some well known properties of finite dimensional systems this result is then applied to study delay independent stability of systems with polytopic uncertainties

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

estimation in the semiparametric accelerated failure time model with missing covariates improving efficiency through augmentation abstractthis article considers linear regression with missing covariates and a right censored outcome we first consider a general two phase outcome sampling design where full covariate information is only ascertained for subjects in phase two and sampling occurs under an independent bernoulli sampling scheme with known subject specific sampling probabilities that depend on phase one information e g survival time failure status and covariates the semiparametric information bound is derived for estimating the regression parameter in this setting we also introduce a more practical class of augmented estimators that is shown to improve asymptotic efficiency over simple but inefficient inverse probability of sampling weighted estimators estimation for known sampling weights and extensions to the case of estimated sampling weights are both considered the allowance for estimated sampling weights permits covariates to be missing at random according to a monotone but unknown mechanism the asymptotic pr

new delay dependent stabilization conditions of t s fuzzy systems with constant delay this paper focuses on the problem of robust control for takagi sugeno t s fuzzy systems with time delay the delay dependent stability analysis and controller synthesis have been addressed the free weighting matrix method has been used for stability analysis and controller synthesis new and less conservative delay dependent stability conditions are proposed in terms of linear matrix inequalities lmi finally some examples are given to illustrate the effectiveness of the proposed approaches

chern classes of tautological sheaves on hilbert schemes of points on surfaces we give an algorithmic description of the action of the chern classes of tautological bundles on the cohomology of hilbert schemes of points on a smooth surface within the framework of nakajima s oscillator algebra this leads to an identification of the cohomology ring of hilb n a2 with a ring of explicitly given differential operators on a fock space we end with the computation of the top segre classes of tautological bundles associated to line bundles on hilb n up to n 7 extending computations of severi lebarz tikhomirov and troshina and give a conjecture for the generating series

parameter dependent robust stability of uncertain time delay systems this paper presents a new delay dependent and parameter dependent robust stability criterion for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state this criterion expressed as a set of linear matrix inequalities requires no matrix variable to be fixed for the entire uncertainty polytope which produces a less conservative stability test result numerical examples are given to show the effectiveness of the proposed techniques

optimal tracking control for large scale interconnected systems with time delays this paper considers an infinite horizon optimal tracking control problem for a class of large scale interconnected systems with state time delays by using the successive approximation approach two iteration sequences of vector differential equations are constructed meanwhile the large scale interconnected system is decomposed into finite decoupled subsystems the existence and uniqueness of the optimal solution is proved as well as the convergence of the solution sequence by finite iterations of the solution sequence a suboptimal tracking control law is obtained a reduced order reference input observer is designed to make the feedforward term of the optimal tracking control law physically realizable a numerical example shows that the presented algorithm is effective and easy to implement

technical communique robust stability of uncertain delay differential systems of neutral type this paper focuses on the stability problem for neutral delay differential systems with norm bounded and possibly time varying uncertainty the time delay is assumed constant and known a stability criterion that is formulated in a linear matrix inequality lmi form is derived numerical examples show that the results obtained by this new criterion significantly improve the estimate of stability limit over some existing results in the literature

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

technical communique delay dependent robust stability for uncertain linear systems with interval time varying delay this paper is concerned with the delay dependent robust stability problem for uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and no restriction on the derivative of the time varying delay is needed which allows the delay to be a fast time varying function the uncertainty under consideration is norm bounded and possibly time varying uncertainty based on the lyapunov krasovskii functional approach a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria numerical examples are given to demonstrate effectiveness of the proposed method

state feedback stabilization of time varying delay uncertain systems a delay decomposition approach abstract this paper focuses on the problem of asymptotic stabilization for time varying delay uncertain systems by developing a delay decomposition approach the information of the delayed plant states can be taken into full consideration and new delay dependent sufficient stabilization criteria are obtained in terms of linear matrix inequalities lmis based on this a delay dependent sufficient condition for the existence of a state feedback controller ensuring stability of the closed loop dynamics is proposed then based on the lyapunov method a delay dependent stabilization criterion is devised by taking the relationship between terms in the leibniz newton formula into account integral inequality approach iia and delay decomposition approach are used to express this relationship and linear matrix inequalities lmis based algorithm to design the controller stabilizing the system