high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

comments on high speed area efficient multiplier design using multiple valued current mode circuits s kawahito et al 1988 presented multiplier designs using the binary tree reduction feature of certain highly redundant radix 2 representations along with multiple valued current mode circuit techniques and shown them to compare favorably to those based on less redundant binary signed digit and carry save numbers we point out that these representation schemes and their potential advantages have been discussed in earlier publications and that a more general view of the parallel carries addition process exploited in these multipliers leads to other potentially useful representations the authors reply is also given

a mixed effects model for multivariate ordinal response data including correlated discrete failure times with ordinal responses the mixed effects model for binary responses due to conaway 1990 a random effects model for binary data is extended to accommodate ordinal responses in general and discrete time survival data with ordinal responses in particular given a multinomial likelihood cumulative complementary log log link function and log gamma random effects distribution the resulting marginal likelihood has a closed form as a result a newton raphson estimation procedure is feasible without resorting to numerical approximation based or monte carlo integration techniques the parameters in the model have a proportional hazards interpretation in terms of multivariate discrete time data with ordinal responses using data from a psychological example the proposed method is compared with other mixed effects approaches as well as population averaged models

nonlinear multilevel models with an application to discrete response data summary a procedure is proposed for the analysis of multilevel nonlinear models using a linearization the case of log linear models for discrete response data is studied in detail nonlinear models arise in a number of circumstances notably when modelling discrete data in this paper we consider the multilevel nonlinear model as in linear multilevel models we shall consider the general case where any of the model coefficients can be random at any level and where the random parameters may also be specified functions of the fixed parameter estimates discussed by h goldstein r prosser and j rasbash in an as yet unpublished report in the next two sections we set out the model and define notation this is followed by a section on estimation and then some examples

area time efficient sign detection technique for binary signed digit number system computer arithmetic operations based on the bsd binary signed digit number representation system lend themselves well to high speed computations due to the facilitation of limited carry addition subtraction we propose an area time efficient method for sign detection in a bsd number system based on optimized reverse tree structure when compared to other popular approaches such as the most significant carry detection based cla carry look ahead and mrc multilevel reverse carry implementations the proposed method is superior to both area and time costs in vlsi synthesis results for different word lengths show that the proposed approach to sign detection in the bsd number system continues to maintain its advantage over area and time measures

scalable estimation and regularization for the logistic normal multinomial model clustered multinomial data are prevalent in a variety of applications such as microbiome studies where metagenomic sequencing data are summarized as multinomial counts for a large number of bacterial taxa per subject count normalization with ad hoc zero adjustment tends to result in poor estimates of abundances for taxa with zero or small counts to account for heterogeneity and overdispersion in such data we suggest using the logistic normal multinomial lnm model with an arbitrary correlation structure to simultaneously estimate the taxa compositions by borrowing information across subjects we overcome the computational difficulties in high dimensions by developing a stochastic approximation em algorithm with hamiltonian monte carlo sampling for scalable parameter estimation in the lnm model the ill conditioning problem due to unstructured covariance is further mitigated by a covariance regularized estimator with a condition number constraint the advantages of the proposed methods are illustrated through simulations and an application to human gut microbiome data

the differential cordic algorithm constant scale factor redundant implementation without correcting iterations the cordic algorithm is a well known iterative method for the efficient computation of vector rotations and trigonometric and hyperbolic functions basically cordic performs a vector rotation which is not a perfect rotation since the vector is also scaled by a constant factor this scaling has to be compensated for following the cordic iteration since cordic implementations using conventional number systems are relatively slow current research has focused on solutions employing redundant number systems which make a much faster implementation possible the problem with these methods is that either the scale factor becomes variable making additional operations necessary to compensate for the scaling or additional iterations are necessary compared to the original algorithm in contrast we developed transformations of the usual cordic algorithm which result in a constant scale factor redundant implementation without additional operations the resulting differential cordic algorithm dcordic makes use of on line most significant digit first redundant computation we derive parallel architectures for the radix 2 redundant number systems and present some implementation results based on logic synthesis of vhdl descriptions produced by a dcordic vhdl generator we finally prove that due to the lack of additional operations dcordic compares favorably with the previously known redundant methods in terms of latency and computational complexity

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

a simple criterion for global stabilizability of a class of nonlinear singularly perturbed systems in this paper a simple criterion is proposed for the global stabilizability of a class of nonlinear singularly perturbed systems our approach is based on the global nonlinear controller canonical transformation and the integral manifold method a globally stabilizing feedback control is also proposed such that the pre specified design manifold becomes an exact slow integral manifold and the trajectories of the closed loop system starting from any initial states are steered along the integral manifold to the origin

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

on the implementation of arithmetic support functions for generalized signed digit number systems ordinary signed digit osd number representation systems have been defined for any radix r or 3 with digit values ranging over the set alpha 1 0 1 alpha where alpha is an arbitrary integer in the range r 2 0 and beta 0 explicitly zero detection sign detection and overflow handling are also treated in depth

brief dichotomic basis approach to solving hyper sensitive optimal control problems as a step toward developing a general method for determining the underlying geometric structure of two time scale optimally controlled nonlinear systems we define a degenerate class of two time scale optimal control problems called completely hypersensitive problems and propose an indirect solution method for this class of problems the method uses a dichotomic basis to split the hamiltonian vector field into its stable and unstable components an accurate approximation to the optimal solution is constructed by matching the initial and terminal boundary layer segments with the equilibrium solution a variation of the method for the case of an approximate dichotomic basis is also developed and is applied to a nonlinear spring mass problem the challenging problem of determining a dichotomic basis or a sufficiently accurate approximation to one is discussed only briefly but some potential solutions are identified

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

feedback control of two time scale nonlinear systems this article concerns a class of two time scale single input single output nonlinear systems for such systems combination of singular perturbation and geometric methods is employed to synthesize well conditioned static state feedback laws that induce a well characterized input output behaviour and guarantee stability of the closed loop system the developed control laws are applied to two nonlinear chemical processes with time scale multiplicity and their performance is evaluated through simulations

comments on evaluation of a b k conditions without carry propagation a special carry free circuit for the evaluation of conditions of the type a b k is proposed by cortadella and llaberia 1992 and its usefulness for reducing the negative effects of conditional branches in pipelined architectures is noted it is shown that the same advantages are offered by another equally simple circuit based on carry save redundant numbers and 3 2 counters this alternative circuit has other potential applications and much of it may in fact be already present in some alu s

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

high speed vlsi multiplication algorithm with a redundant binary addition tree a high speed vlsi multiplication algorithm internally using redundant binary representation is proposed in n bit binary integer multiplication n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders since parallel addition of two n digit redundant binary numbers can be performed in a constant time independent of n without carry propagation n bit multiplication can be performed in a time proportional to log2 n the computation time is almost the same as that by a multiplier with a wallace tree in which three partial products will be converted into two in contrast to our two to one conversion and is much shorter than that by an array multiplier for longer operands the number of computation elements of an n bit multiplier based on the algorithm is proportional to n2 it is almost the same as those of conventional ones furthermore since the multiplier has a regular cellular array structure similar to an array multiplier it is suitable for vlsi implementation thus the multiplier is excellent in both computation speed and regularity in layout it can be implemented on a vlsi chip with an area proportional to n2 log2 n the algorithm can be directly applied to both unsigned and 2 s complement binary integer multiplication

signed digit representations of minimal hamming weight the authors give an online algorithm for computing a canonical signed digit representation of minimal hamming weight for any integer n using combinatorial techniques the probability distributions pr k sub r h where k sub r is taken to be a random variable on the uniform probability space of k digit integers is computed also using a markov chain analysis it is shown that e k sub r approximately r 1 k r 1 as k to infinity

composite feedback control for a class of non linear singularly perturbed systems with fast actuators a design methodology for a class of non linear singularly perturbed systems with fast actuators is proposed using the composite control technique the origin of the nominally unforced unperturbed system is assumed to be asymptotically stable and a lyapunov function for the nominal system is available then by appropriate choice of the design manifold a composite feedback control can be constructed to guarantee the asymptotic stability of the origin of the closed loop system

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

continuity of singular perturbations in the graph topology abstract for a certain model for singular perturbations in control systems which we motivate by a simple example we show that under weak assumptions continuity in the graph topology holds as the perturbation parameter tends to zero this may be contrasted with a result by cobb who considered a different model for singular perturbations and who found a strong condition to be necessary for continuity in that model our proof techniques are based on the characterization due to qiu and davison of the graph topology as a topology of uniform convergence

weak connections time scales and aggregation of nonlinear systems if nonlinear subsystems with continuous equilibria are weakly connected their local behavior is fast compared with the system wide behavior caused by the connections the slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model in this way earlier linear aggregation results by simon et al in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations

generalized signed digit number systems a unifying framework for redundant number representations signed digit sd number representation systems have been defined for any radix r or 3 with digit values ranging over the set alpha 1 0 1 alpha where alpha is an arbitrary integer in the range 1 2r

efficient exponentiation of a primitive root in gf 2 sup m in this paper exponentiation of a primitive root in gf 2 sup m is considered signed digit sd number representation is used to efficiently represent the exponent and the corresponding algorithms and structures for exponentiation are developed for primitive multiplications required in exponentiations extended bidirectional linear feedback shift registers are proposed and used for the cases where the exponent is represented as a binary or a radix 4 sd number comparisons are made with other methods on the bases of space time and possible power consumption since the proposed structures can effectively reduce power and area when implemented in vlsi they are especially suitable for battery powered portable devices

trend in correlated proportions a random effects probit model is developed for the case in which the same units are sampled repeatedly at each level of an independent variable because the observed proportions may be correlated under these conditions estimating their trend with respect to the independent variable is no longer a standard problem for probit logit or loglinear analysis using a qualitative analogue of a random regressions model we employ instead marginal maximum likelihood to estimate the average latent trend line likelihood ratio tests of the hypothesis of no trend in the average line and the hypothesis of no differences in average trend lines between experimental treatments are proposed we illustrate the model both with simulated data and with observed data from a clinical experiment in which psychiatric patients on two drug therapies are rated on five occasions for the presence or absence of symptoms

double step branching cordic a new algorithm for fast sine and cosine generation duprat and muller 1993 introduced the ingenious branching cordic algorithm it enables a fast implementation of cordic algorithm using signed digits and requires a constant normalization factor the speedup is achieved by performing two basic cordic rotations in parallel in two separate modules in their method both modules perform identical computation except when the algorithm is in a branching 1 we have improved the algorithm and show that it is possible to perform two circular mode rotations in a single step with little additional hardware in our method both modules perform distinct computations at each step which leads to a better utilization of the hardware and the possibility of further speedup over the original method architectures for vlsi implementation of our algorithm are discussed

a new symbolic substitution based addition algorithm symbolic substitution a parallel processing technique has been proposed in computing literature to perform fast carry free addition of numbers several algorithms and corresponding symbolic substitution tables have been developed for addition of two numbers represented in binary modified signed digit msd and canonical modified signed digit cmsd number systems in this paper however we present a new symbolic substitution based algorithm and corresponding substitution table for the addition of two numbers represented in canonical modified signed digit cmsd notation in contrast with the existing algorithm in this regard that derives the addition result in msd system our algorithm derives the result in cmsd notation and thus it could be employed to perform symbolic substitution based associative addition of a set of cmsd numbers

a proportional odds model with subject specific effects for repeated ordered categorical responses summary suppose subjects make repeated responses on the same ordered categorical scale we propose a generalization of the rasch model that expresses the cumulative logit of the response distribution using subject parameters and a proportional odds structure for item effects parameters in the model describe subject specific rather than populationaveraged effects consistent estimation of the effects requires eliminating the subject parameters we accomplish this by simultaneous fitting of rasch models conditional on sufficient statistics for those parameters for the possible binary collapsings of the response the fitting process uses an improved newton raphson algorithm for fitting generalized loglinear models by maximum likelihood estimation subject to constraints for the case of two items we give simple expressions for an effect estimate and its standard error and suggest a test of marginal homogeneity for ordinal matched pairs

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

constant time addition and simultaneous format conversion based on redundant binary representations it is well known that constant time addition in which the execution delay is independent of operand lengths is feasible only if the output is expressed in a redundant representation there are many ways of introducing redundancy and the specifics of the redundant format employed can have a major impact on the performance of constant time addition and digit set conversion this paper presents a comprehensive analysis of constant time addition and simultaneous format conversion we consider full as well as partially redundant representations where not all digit positions are redundant the number of redundant digits and their positions can be arbitrary yielding many possible redundant representations format conversion refers to changing the number and or position of redundant digits in a representation it is shown that such a format conversion is feasible during ie simultaneous with constant time addition even if all three operands the two inputs and single output are represented in distinct redundant formats we exploit equal weight grouping ewg wherein bits having the same weight are grouped together to achieve the constant time addition and possible simultaneous format conversion the analysis and data show that ewg leads to efficient implementations we compare vlsi implementations of various constant time addition cells and demonstrate that the conventional 4 2 compressor is the most efficient way to execute constant time addition we show interesting connections to prior results and indicate possible directions for further extensions

on the connection between nonlinear differential algebraic equations and singularly perturbed control systems in nonstandard form considers a class of control systems represented by nonlinear differential equations depending on a small parameter the systems are not in the standard singularly perturbed form and therefore one of the challenges is to show that the control systems do represent singularly perturbed two time scale systems assumptions are introduced which guarantee that an equivalent representation for the systems can be obtained in the standard singularly perturbed form thereby justifying the two time scale property the equations for the slow dynamics are characterized by a set of differential algebraic equations which have been studied previosly in the literature the fast dynamics are characterized by differential equations both the slow and the fast dynamics are easily derived and are defined in terms of variables that define the original control system control design for the class of systems being considered is studied using the composite control approach

certain discrete dynamical systems number systems and related integral self affine sets we consider certain discrete dynamical systems conventional number systems and redundant number systems for z 2 which are associated with certain 2x2 integral expansive matrices and collinear digit sets for them using integral self affine sets in r n we also give a geometric characterization to attractors of certain discrete dynamical systems and associated redundant number systems for z n

a simple criterion for global exponential stabilizability of nonlinear multiple time delay singularly perturbed systems a simple criterion for global exponential stability of a class of nonlinear multiple time delay singularly perturbed systems without the so called interconnection conditions is proposed in this paper a globally exponentially stabilizing composite feedback control is also proposed such that the chosen design manifold becomes an exact integral manifold and the trajectories of the closed loop systems starting from any initial states are steered along the integral manifold to the origin exponentially for all sufficiently small singular perturbation parameters e the composite control technique is adopted in this paper

high radix multiplier dividers theory design and hardware this paper describes the theory and design of digital high radix multiplier dividers patent pending the theory of high radix division is extended to high radix multiplier dividers that can perform fused multiplication and division operations using a single recurrence relation with the fused implementation of multiplication and division the two operations can be executed using a single instruction implying only a single rounding operation the recurrence relation is described the quotient digit selection function derived and important design parameters together with their optimal values and relations are defined efficient design procedure and implementation hardware are described and important system parameter values for various radix systems computed compared to pure dividers the multiplier divider requires a slightly more complex data path and quotient digit selection function

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

a random effects ordinal regression model for multilevel analysis a random effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data this model is developed for both the probit and logistic response functions the threshold concept is used in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects a maximum marginal likelihood mml solution is described using gauss hermite quadrature to numerically integrate over the distribution of random effects an analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random effects analysis of clustered ordinal data while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random effects approach for longitudinal ordinal data

hybrid signed digit number systems a unified framework for redundant number representations with bounded carry propagation chains a novel hybrid number representation is proposed it includes the two s complement representation and the signed digit representation as special cases the hybrid number representations proposed are capable of bounding the maximum length of carry propagation chains during addition to any desired value between 1 and the entire word length the framework reveals a continuum of number representations between the two extremes of two s complement and signed digit number systems and allows a unified performance analysis of the entire spectrum of implementations of adders multipliers and alike we present several static cmos implementations of a two operand adder which employ the proposed representations we then derive quantitative estimates of area in terms of the required number of transistors and the maximum carry propagation delay for such an adder the analysis clearly illustrates the trade offs between area and execution time associated with each of the possible representations we also discuss adder trees for parallel multipliers and show that the proposed representations lead to compact adder trees with fast execution times in practice the area available to a designer is often limited in such cases the designer can select the particular hybrid representation that yields the most suitable implementation fastest lowest power consumption etc while satisfying the area constraint similarly if the worst case delay is predetermined the designer can select a hybrid representation that minimizes area or power under the delay constraint

non standard singularly perturbed control systems and differential algebraic equations we consider a class of linear control systems represented by equations depending on a small parameter but which are not in the standard singularly perturbed form one of the challenging system theoretic problem is to obtain an equivalent representation for the control system which if possible is in the standard singularly perturbed form assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form thereby justifying the two time scale property the equations for the slow dynamics are characterized by a set of differential algebraic equations which are easily derived from the original equations by setting the parameter to zero the original assumptions guarantee the existence of solutions of the obtained differential algebraic equations the fast dynamics are characterized by different equations in terms of matrices that define the original control system control design for the system being considered is studied using th

reviewing high radix signed digit adders higher radix values of the form beta 2 r have been employed traditionally for recoding of multipliers and for determining quotient and root digits in iterative division and square root algorithms usually only for quite moderate values of r like 2 or 3 for fast additions in particular for the accumulation of many terms generally redundant representations are employed most often binary carry save or borrow save but in a number of publications it has been suggested to recode the addends into a higher radix it is shown that there are no speed advantages in doing so if the radix is a power of 2 on the contrary there are significant savings in using standard 4 to 2 adders even saving half of the operations in multi operand addition

signed binary addition circuitry with inherent even parity outputs a signed binary se addition circuit is presented that always produces an even parity representation of the sum word the novelty of this design is that no extra check bits are generated or used the redundancy inherent in a se representation is further exploited to contain parity information

a geometric approach to nonlinear singularly perturbed control systems abstract applications of two time scale singular perturbation methods have been limited to the class of models appearing in a standard form many nonlinear control systems such as models of aircraft and robotic manipulators with flexible joints are two time scale systems but do not appear in the standard form the main result of this paper is a coordinate free characterization of time scales in terms of invariant manifolds which express conservation and equilibrium properties of the control system a procedure for finding slow and fast states is given previously developed slow fast composite control designs are thus made applicable to a wider class of nonlinear systems

digit set conversions generalizations and applications the problem of digit set conversion for fixed radix is investigated for the case of converting into a non redundant as well as into a redundant digit set conversion may be from very general digit sets and covers as special cases multiplier recodings additions and certain multiplications we generalize known algorithms for conversions into non redundant digit sets as well as apply conversion to generalize the o log n time algorithm for conditional sum addition using parallel prefix computation and a comparison is made with standard carry lookahead techniques examples on multi operand addition are used to illustrate the generality of this approach o 1 time algorithms for converting into redundant digit sets are generalized based on a very simple lemma which provides a framework for all conversions into redundant digit sets applications in multiplier recoding and partial product accumulation are used as exemplifications

nonlinear control of a bioreactor model using exact and i o linearization a nonlinear multivariable bioreactor system has been the subject of two differential geometry feedback control design approaches exact linearization and input output linearization are applied to the bioreactor model and verified by simulation experiments exact linearization via state feedback shows a high degree of coupling on the controlled variables and large changes on the manipulated variables input output linearization with the ability of implementing independent decoupled control loops gives more satisfactory results the issues of invertabiity and parameter uncertainties are also discussed in this paper

carry free addition of recoded binary signed digit numbers signed digital number representation systems have been defined for any radix r or 3 with digit values ranging over the set alpha 1 0 1 alpha where alpha is an arbitrary integer in the range r 2

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

a mixed effects multinomial logistic regression model a mixed effects multinomial logistic regression model is described for analysis of clustered or longitudinal nominal or ordinal response data the model is parameterized to allow flexibility in the choice of contrasts used to represent comparisons across the response categories estimation is achieved using a maximum marginal likelihood mml solution that uses quadrature to numerically integrate over the distribution of random effects an analysis of a psychiatric data set in which homeless adults with serious mental illness are repeatedly classified in terms of their living arrangement is used to illustrate features of the model

a random effects model for ordinal responses from a crossover trial crossover studies have been successfully conducted in the case of continuous responses existing procedures of analysis for ordinal responses on the other hand are rarely satisfactory unless strict usually unrealistic assumptions are made in this paper we investigate a random effects model and show that the model is simple and general interpretation of parameters is easy though with a complicated fitting procedure

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

comments on duprat and muller s branching cordic paper duprat and muller ieee trans computers vo1 42 no 2 p 168 178 feb 1993 introduced the ingenious branching cordic algorithm it enables a fast implementation of cordic algorithm using signed digits and requires a constant normalization factor this correspondence corrects some errors in the original paper

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures