continuous discrete time observers for a class of mimo nonlinear systems this technical note addresses the observer design problem for a class of continuous time dynamical systems with non uniformly sampled measurements more specifically we propose an observer that runs in continuous time with an output error correction term that is updated in a mixed continuous discrete fashion the proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates nevertheless we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous time high gain observer coupled with an inter sample output predictor two design features of the proposed observer are worth emphasizing firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer

statistical inference with data dependent treatment allocation rules abstract in comparing two treatments with dichotomous responses the randomized play the winner rule wei and durham 1978 tends to assign more study subjects to the better treatment for ethical reasons this property is desirable for studies on human subjects the randomized play the winner rule which is a modification of zelen s play the winner rule zelen 1969 is not deterministic and is less vulnerable to experimental bias than other adaptive designs recently this design has been used in a trial to evaluate extracorporeal membrane oxygenation ecmo for treating newborns with respiratory failures at the university of michigan in this article exact conditional exact unconditional and approximate confidence intervals for the treatment difference are studied from a frequentist point of view with the randomized play the winner rule for small and moderate sized trials the exact unconditional procedures perform much better than the conditional ones because of the adaptive nature of the designs

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control

universal presheaves on group geometries and modular representations abstract we extend the ideas of sheaf homology on buildings m a ronan and s d smith j algebra 96 1985 319 346 to more general geometries with transitive automorphism groups the main technical result is the construction of a universal extension of certain partial sheaves this guarantees a rich supply of sheaves on such geometries computation of zero homology then affords representations of the group we consider various applications of the technique for example to modular irreducibles for sporadic simple groups

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

observer design for a special class of nonlinear systems in this paper we present the design of an observer for a special class of nonlinear systems satisfying some regularity assumptions in both the single output and multioutput case the controlled part of the considered systems have a triangular structure a further extension of the design strategy is made to a specific class of multioutput systems which assume stronger nonlinear dependence between the various subsystems the design is illustrated by a simulation experiment dealing with rotor flux estimation in an induction motor

adaptive observer for multiple input multiple output mimo linear time varying systems for joint state parameter estimation in linear time varying ltv multiple input multiple output mimo systems an approach to the design of adaptive observers is proposed it is conceptually simple and computationally efficient its global exponential convergence is established for noise free systems in the presence of noises it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means potential applications are fault detection and isolation and adaptive control

a chain observer for nonlinear systems with multiple time varying measurement delays this paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time varying delays a modular approach is followed where subobservers are connected in cascade to achieve a desired exponential convergence rate chain observer when the delay is small a single step observer is sufficient to carry out the goal two or more subobservers are needed in the the presence of large delays the observer employs delay dependent time varying gains to achieve the desired exponential error decay the proposed approach allows to deal with vector output measurements where each output component can be affected by a different delay relationships among the error decay rate the bound on the measurement delays the observer gains and the lipschitz constants of the system are presented the method is illustrated on the synchronization problem of continuous time hyperchaotic systems with buffered measurements

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

brief paper adaptive observers for nonlinearly parameterized class of nonlinear systems in this paper one proposes adaptive observers for a class of uniformly observable mimo nonlinear systems with general nonlinear parameterizations the state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well defined persistent excitation condition moreover the gain of the observers involves a design function that has to satisfy a simple condition which is given different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function the theory is supported by simulation results related to the estimation of the biomass concentration and the contois model parameters in a bioreactor

a cascade observer for a class of mimo non uniformly observable systems with delayed sampled outputs abstract this paper investigates the observation problem for a class of mimo non uniformly observable systems in the presence of sampled and delayed outputs a high gain observer is first designed for the delay free and continuous output measurement case the observer gain involves the resolution of an appropriate lyapunov differential equation allowing to show that the underlying observation error converges exponentially to zero under a well defined persistent excitation condition this observer is then redesigned to cope with the output sampling process as well as the output delay thanks to an appropriate cascade structure composed of a set of dynamical subsystems the first subsystem in the cascade is an impulsive continuous discrete time observer which provides the estimation of the delayed state and each remaining subsystem in the cascade is a predictor which estimates the state over a small horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state the exponential convergence to zero of the observation error related to the cascade observer is established for arbitrarily long delays provided that the maximum value of the sampling partition diameter is lower than a certain given bound simulations results are given to highlight the performance and the main properties of the proposed cascade observer

a note on design when response has an exponential family distribution summary some simple design problems are considered when responses have an exponential family distribution with the difference between treatment groups in the canonical parameter being the objective of study it is shown that normal theory conclusions apply to a possibly surprising extent the loss from randomizing followed by subsequent stratification is the equivalent of one observation per stratum for binary data heterogeneity has to be quite large before failure to stratify induces serious loss whereas unnecessary use of a matched pair design is fully efficient asymptotically

observer design for mimo non uniformly observable systems the design of high gain observers is usually based on normal forms of observability if the system is observable for every input uniform observability the gain of the observer does not required a solution to differential equation for multiple input multiple output mimo non uniformly observable systems we give here a sufficient condition that the input must satisfy in order to design an observer unlike uniformly observable systems the observer gain of non uniformly observable systems is derived from a lyapunov differential equation

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

adaptive biased coin designs for skewing the allocation proportion in clinical trials with normal responses response adaptive designs are used in phase iii clinical trial for skewing the allocation pattern towards the better treatments we use optimum design theory to derive adaptive designs when the responses are normally distributed the performance of the designs is studied with respect to the loss and the proportion of allocation to different treatments the adaptive design does not affect inference

shift invariant target in allocation problems we provide a template for finding target allocation proportions in optimal allocation designs where the target will be invariant for both shifts in location and scale of the response distributions one possible application of such target allocation proportions is to carry out a response adaptive allocation while most of the existing designs are invariant for any change in scale of the underlying distributions they are not location invariant in most of the cases first we indicate this serious flaw in the existing literature and illustrate how this lack of location invariance makes the performance of the designs very poor in terms of allocation for any drastic change in location such as the changes from degrees centigrade to degrees fahrenheit we illustrate that unless a target allocation is location invariant it might lead to a completely irrelevant and useless target for allocation then we discuss how such location invariance can be achieved for general continuous responses we illustrate the proposed method using some real clinical trial data we also indicate the possible extension of the procedure for more than two treatments at hand and in the presence of covariates

stability of polymerization reactors using i o linearization and a high gain observer we develop an observer based control structure for a standard nonlinear model of polymerization reactors we use a classical input output linearization technique for the controller synthesis and prove theoretically its global asymptotic stability because our stabilizing feedback laws require knowledge of the state of the model we solve the estimation problem by designing an exponentially converging observer the equations of which are close to those of the extended kalman filter finally by proving a nonlinear separation principle we conclude that our observer based control structure is capable of stabilizing polymerization reactors as a consequence polymerization reactors can be operated even on open loop unstable steady states

simple cascade observer for a class of nonlinear systems with long output delays this note proposes a cascade observer for a class of nonlinear systems with global lipschitz nonlinearities in the presence of delayed output measurements the head of the cascade is a high gain observer while the remaining systems are state predictors providing an estimate of the actual state the key feature of the proposed observer is the introduction of a matrix design parameter that allows to tune the prediction process dominant dynamics with an identical simple structure for all the predictors the design of the observer is carried out by considering a set of conditions under which the exponential convergence to zero of the observation error is established in particular it is shown that the number of the subsystems in the cascade observer depends on the size of the delay and the lipschitz constant the observer is first designed assuming a constant time delay the underlying design approach is then appropriately adapted to deal with the time varying delay the effectiveness of the proposed observer with respect to two existing cascade observers is particularly highlighted through a comprehensive comparative analysis and simulation results

an immersion based observer design for rank observable nonlinear systems in this note an observer design for a wide class of nonlinear systems is proposed it is based on some high gain design for the particular case of state affine systems up to triangular nonlinearity on the one hand and immersion of nonlinear systems into such a form on the other hand conditions for the observer convergence are given in terms of appropriate excitation and a constructive procedure for the immersion is presented the methodology is illustrated by examples of application

from continuous time design to sampled data design of observers in this work a sampled data nonlinear observer is designed using a continuous time design coupled with an inter sample output predictor the proposed sampled data observer is a hybrid system it is shown that under certain conditions the robustness properties of the continuous time design are inherited by the sampled data design as long as the sampling period is not too large the approach is applied to linear systems and to triangular globally lipschitz systems

brief adaptive estimation of discrete time systems with nonlinear parameterization this paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized a majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment which ensures stable estimation when parameters occur linearly these algorithms however do not suffice for estimation in systems with nonlinear parameterization we introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size both concave convex parameterizations as well as general nonlinear parameterizations are considered stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established for the case of concave convex parameterizations parameter convergence is shown to result under certain conditions of persistent excitation

classical locally finite tits chamber systems of rank 3 a chamber system v 9 j zi is over some index set z is a set of chambers together with partitions in z of v if ze z and c e v then bj is the join of all partitions fijzi e z and d c is the element of fij containing c d c is again a chamber system over j with fij restricted to z we say q is connected if d c furthermore 111 is the rank of v the most important examples of chamber systems are those obtained from groups if g is a group b a subgroup of g and xi ie z are subgroups of g containing b then 5 g b xi icl has as chambers the cosets bg g e g two such cosets bg bh being i adjacent if and only if xi g xih then g acts chamber transitively on with kernel b n bg and is connected if and only if g x 1 i e z furthermore each chamber system with transitive automorphism group g can be obtained in this way by setting b g and xi gd cr a rank 2 chamber system u hi fi is called a classical generalized ma gon mq 3 if is isomorphic to g b pi p where g is an essentially simple rank 2 group of lie type in the sense of cl b is a bore1 subgroup and p pj are the two maximal parabolic subgroups of g containing b here md is given by the relation vu wj wiw g 1 defined by the weyl group of g a rank 2 chamber system is a generalized digon if is isomorphic to v g pin p pi p where pi p are different proper subgroups of g satisfying g pipj pjpi a connected chamber system over z is called a classical tits chamber system if for each ce and i j c z di j c is either a generalized digon or a classical generalized m gon for some mi e n is focally finite if all d c are finite for motivation to consider such classical locally finite tits chamber systems see 15 and 16 if is a classical tits chamber system then the diagram d z is defined in 9 0021 8693 89 3 00

observer design for a class of mimo nonlinear systems a simple observer is proposed for a large class of mimo nonlinear systems which includes many physical models the main characteristic of the proposed observer lies in the easiness of its implementation and calibration indeed the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given moreover its calibration is achieved through the choice of a single parameter a simulation example is given in order to illustrate the performance of the proposed observer

stable adaptive observers for nonlinear time varying systems an adaptive observer identifier for single input single output observable nonlinear systems that can be transformed to a certain observable canonical form is described sufficient conditions for stability of this observer are provided these conditions are in terms of the structure of the system and canonical form the boundedness of the parameter variations and the sufficient richness of some signals the scope of the canonical form and the use of the observer identifier is motivated by the presentation of applications to time invariant bilinear systems nonlinear systems in phase variable form a biotechnological process and a robot manipulator in each case the specific stability conditions are presented

saturated fusion systems with parabolic families abstract let g be a group a finite p subgroup s of g is a sylow p subgroup if every finite p subgroup of g is conjugate to a subgroup of s in this paper we examine the relations between the fusion system over s which is given by conjugation in g and a certain chamber system c on which g acts chamber transitively with chamber stabilizer n g s next we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system we determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system we give an application to fusion systems with parabolic families of classical type

a 3 local identification of two almost simple extensions of pω8 2 abstract we provide 3 local characterizations of the almost simple groups p 8 2 3 and p 8 2 sym 3 both groups are examples of groups of parabolic characteristic three and we identify them from the structure of the centralizer of an element of order three

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

extended high gain observer design for a class of mimo non uniformly observable systems abstract this paper deals with the design of an extended high gain observer ehgo for a large class of multiple input multiple output mimo non uniformly observable systems indeed the involved system nonlinearities does not assume the usual triangular structure as it is often the case when a high gain approach is adopted this structure constraint relaxation is achieved by an appropriate use of the characteristic indices associated to the state components there are two fundamental features that are worth to be pointed out firstly the gain of the proposed ehgo is provided by an appropriate riccati ordinary differential equation ode secondly the convergence of the observation error is guaranteed under some persistent excitation condition which can be checked on line simulation results are given to illustrate the performance of the proposed ehgo

global exponential sampled data observers for nonlinear systems with delayed measurements abstract this paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements by using a small gain approach we provide sufficient conditions which involve both the delay and the sampling period ensuring exponential convergence of the observer system error the proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule moreover new results on the robust global exponential state predictor design problem are provided for wide classes of nonlinear systems

optimum biased coin designs for sequential clinical trials with prognostic factors patients in a clinical trial arrive sequentially and are assigned to one of t treatments this assignment should maintain a balance between the numbers receiving each treatment yet should be sufficiently random to avoid any suspicion of conscious or unconscious cheating to balance these requirements efron 1971 introduced biased coin designs for the comparison of two treatments in which allocation of the treatment is determined probabilistically but with a bias towards the underrepresented treatment one disadvantage of efron s scheme is that it does not include balance over covariates or prognostic factors which may affect the response of the patient to the treatment biased coin schemes which do force balance over both treatments and prognostic factors are given by pocock simon 1975 and efron 1980 the properties of the designs have been elucidated by numerical studies and they are now being increasingly used in clinical trials reviews of the literature and discussions of the practical implications of the designs are given by pocock 1979 and simon 1979 however the designs suffer from the disadvantage that they rely on arbitrary functions to achieve the desired balance the procedures thus lack a firm theoretical framework an alternative approach in the presence of prognostic factors begg iglewicz 1980 uses optimum design theory to suggest a deterministic design criterion which is then modified for computational convenience in this paper i use optimum design theory to provide a procedure of the biased coin type for an arbitrary number of treatments in the presence or absence of prognostic factors this has the theoretical advantage of obviating dependence on a series of arbitrary functions the necessary optimum design theory is presented in 2 and in 3 applied to biased coin experiments the simplest case that of two treatments in the absence of prognostic factors is studied in 4 the extension to three or more treatments is in 5 followed in 6 by the allowance for prognostic factors although in the biased coin designs allocation of treatments is made probabilistically the results of the paper can be used for the sequential construction of da optimum designs in which randomization is not introduced by the experimenter all the designs mentioned so far are sequential but not adaptive in the useful distinction made by pericchi 1981 they are data dependent but not outcomedependent each allocation depends on the previous allocations and prognostic factors

nonlinear system fault diagnosis based on adaptive estimation an approach to fault diagnosis for a class of nonlinear systems is proposed in this paper it is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults this algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer without resort to any linearization its global exponential convergence is ensured by an easy to check persistent excitation condition a numerical example is presented for illustration

bias and loss the two sides of a biased coin the paper assesses biased coin designs for sequential treatment allocation in clinical trials comparisons emphasise the importance of considering randomness as well as treatment balance which are calculated as bias and loss in the numerical examples the responses are assumed normally distributed perhaps after transformation and balance is required over a set of covariates the effect of covariate distribution on the properties of five allocation rules is investigated with an emphasis on methods of comparison which also apply to other forms of response the concept of admissibility shows that the widely used minimisation rule is outperformed by atkinson s rule derived from the theory of optimum experimental design we present a simplified form of this rule for this rule the ability to guess the next treatment allocation decreases with study size for the other rules it is constant

high gain estimation for nonlinear systems abstract this work is a continuation of 4 where the third author exhibits a high gain exponential observer for miso nonlinear systems affine in the input and observable for any input with continuous dynamics and measurements in this paper we establish stability results for continuous continuous and continuous discrete extended kalman filters derived from the observer of 4

a geometric presentation for the adjoint module of sl3 k abstract let k be a field the points and lines of the projective plane p k 3 determine corresponding subspaces in the space of 3 3 traceless matrices the adjoint module for the group sl 3 k we show that these subspaces conversely determine the module as their direct limit modulo derivations of the field k

asymptotic properties of covariate adjusted response adaptive designs response adaptive designs have been extensively studied and used in clinical trials however there is a lack of a comprehensive study of response adaptive designs that include covariates despite their importance in clinical trials because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates covariate adjusted response adaptive cara designs are very complex to formulate in this paper we overcome the technical hurdles and lay out a framework for general cara designs for the allocation of subjects to k 2 treatments the asymptotic properties are studied under certain widely satisfied conditions the proposed cara designs can be applied to generalized linear models two important special cases the linear model and the logistic regression model are considered in detail

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

parabolic systems the gf 3 case parabolic systems defined over gf q have been classified by timmesfeld for q 4 and by stroth for q 2 see references we deal with the case q 3

observer design for uniformly observable systems with sampled measurements this work considers the problem of observer design for continuous time systems with sampled output measurements continuous discrete time systems in classical literature and in many applications the continuous discrete time extended kalman filter ekf is used in order to tackle this problem in this work using a normal form characterizing the class of nonlinear uniformly observable single output nonlinear systems it is shown that a particular stationary solution of a continuous discrete time lyapunov equation can be used in order to design a constant high gain observer explicit conditions are given to ensure global convergence of the observer finally an illustration of this result is given using an example of a biological process

a pushing up result and some consequences for the embedding of 2 constrained subgroups let m m1 be maximal 2 locai subgroups of some finite group g with o g 1 satisfying qi o mi f mi for i 0 1 is it possible in this situation that q1 qo the bulk of the proof of l consists of showing that there exists no k group g of characteristic 2 type satisfying these and certain non generational conditions for mi which by results of g seitz strongly restrict the structure of mr if one tries to consider this problem more generally one realizes that it splits naturally into two cases

bayesian adaptive biased coin designs for clinical trials with normal responses des schemas adaptatifs sont utilises dans des essais cliniques de phase iii pour biaiser l attribution des traitements en faveur des meilleurs nous utilisons la theorie des schemas optimaux pour etablir une procedure bayesienne de tirage au sort biaise pour des schemas sequentiels avec reponses continues la performance de ces schemas adaptatifs est etudiee a la fois numeriquement et theoriquement des proprietes importantes sont la perte et la proportion de sujets alloues au meilleur traitement

asymptotic properties of adaptive designs for clinical trials with delayed response for adaptive clinical trials using a generalized friedman s urn design we derive the limiting distribution of the urn composition under staggered entry and delayed response the stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient s response a very general setup is employed with k treatments and l responses when l k 2 one example of a generalized friedman s urn design is the randomized playthe winner rule an application of this rule occurred in a clinical trial of depression which had staggered entry and delayed response we show that maximum likelihood estimators from such a trial have the usual asymptotic properties

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

implementing optimal allocation in sequential binary response experiments for sequential experiments with k treatments we establish two formal optimization criteria to find optimal allocation strategies both criteria involve the sample sizes on each treatment and a concave noncentrality parameter from a multivariate test we show that these two criteria are equivalent we apply this result to specific questions 1 how do we maximize power of a multivariate test of homogeneity with binary response and 2 for fixed power how do we minimize expected treatment failures because the solutions depend on unknown parameters we describe a response adaptive randomization procedure that targets the optimal allocation and provides increases in power along the lines of 2 4 over complete randomization for equal allocation the increase in power contradicts the conclusions of other authors who have explored other randomization procedures for k 2 and have found that the variability induced by randomization negates any benefit of targeting an optimal allocation

on inferences from wei s biased coin design for clinical trials wei 1988 analyzed data from a clinical trial in which an urn sampling model was used to allocate patients to treatments the trial resulted in 11 patients being allocated to the experimental treatment all successes and with one patient allocated to the control treatment a failure wei analyzed these data using a randomization algorithm and concluded that the results were almost significant at p 0 051 he asserted that an analysis which ignored the design and presumed complete randomization leads to a p value of 0 001 in fact if a more conventional analysis is used in which both margins are fixed then this leads to p 0 083 fisher s exact test if complete randomization is assumed if the urn sampling allocation is taken into account much more conservative inferences are obtained an analysis which conditions on both margins leads to p 028 while one which conditions on the observed sequence of responses and the observed treatment totals leads to p 0 62 these serious discrepancies are discussed in addition to the inappropriateness of biased coin design and small sample sizes in important medical trials

optimality variability power we provide a theoretical template for the comparison of response adaptive randomization procedures for clinical trials using a taylor expansion of the noncentrality parameter of the usual chi squared test for binary responses we show explicitly the relationship among the target allocation proportion the bias of the randomization procedure from that target and the variability induced by the randomization procedure we also generalize this relationship for more than two treatments under various multivariate alternatives this formulation allows us to directly evaluate and compare different response adaptive randomization procedures and different target allocations in terms of power and expected treatment failure rate without relying on simulation for k 2 treatments we compare four response adaptive randomization procedures and three target allocations based on multiple objective optimality criteria we conclude that the drop the loser rule and the doubly adaptive biased coin design are clearly super

irreducible modules and parabolic subgroups summary it seems desirable from the point of view of finite group theorists to develop further the representation theory of finite chevalley groups in the characteristic of their definition say p by focusing attention on the full array of p local subgroups that is the parabolics rather than the usual single borel or cartan subgroup the following observation may be regarded as a generalization to arbitrary parabolic subgroups of the standard result 3 theorem 39 d for a borel subgroup namely that in an irreducible module the subspace fixed by a maximal unipotent subgroup is 1 dimensional and so affords an irreducible module for a levi complement which is an abelian cartan subgroup it seems natural to state the result first for algebraic groups

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

lyapunov stability analysis for nonlinear delay systems abstract sufficient conditions ensuring that a nonlinear system with disturbances having a delay is globally asymptotically stable independent of delay are given the proof carried out relies extensively on a characterization of the stability property in terms of lyapunov function the result is applied to some biological systems and neural networks a stabilizing memoryless controller for a second order system with state delay is also proposed

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

adaptive designs for normal responses with prognostic factors summary adaptive designs are often used in clinical trials to force balance in sequential allocation of patients between two or more competitive treatments sometimes from ethical considerations the goal may be to allocate a larger number of patients to the better treatment in the course of the trial in the present paper we consider patients who are heterogeneous with respect to some prognostic factors and assume that the response from each patient is a continuous variable we consider a normal linear model and provide an allocation design with due attention to the prognostic factors the loss of efficiency incurred by using a balanced design is also indicated issues of inference based on adaptive allocation are also discussed finally a guideline is provided for the appropriate choice of the design parameters

sheaf homology and complete reducibility abstract in the study of finite simple groups by means of the geometries provided by their local subgroups problems of structure often reduce to questions about modular representations in finite characteristic of particular interest are modules spanned by fixed points of sylow groups including high weight modules for chevalley groups for which the homology methods of ronan and smith 6 can be very useful this note presents an elementary sufficient condition for splitting of some reducible modules of this type among the applications we generalize a number of results appearing in recent work of timmesfeld 11 which provided the original inspiration for this analysis some of the ideas had appeared in a special case in 10

exact two sample permutation tests based on the randomized play the winner rule in comparing two treatments in a clinical trial the randomized play the winner rule tends to assign more study subjects to the better treatment it is applicable when patients have delayed responses to treatments it is not deterministic and is less vulnerable to experimental bias than other adaptive designs in this paper an efficient algorithm is provided to construct exact permutation tests for testing the equality of the two treatments with the randomized play the winner rule the test procedure is illustrated with a real life example the example shows that the design used in the trial should not be ignored in the analysis

high gain observer design for some networked control systems new results on high gain observer design for networked control systems via an emulation like approach are presented by using a general framework and a lyapunov approach we derive some explicit conditions on the maximum allowable transmission interval that ensure an exponential convergence of the observation error for a large class of network protocols