multiplicative and additive models with external controls in a cohort study of cancer mortality the use of additive and multiplicative hazard models is examined for a cohort study of 2696 women followed up for 12 years the multiplicative model implied that women with a haemoglobin level less than 12 g dl were at higher risk from cancer and the additive model showed that this risk was confined to women after the menopause despite difficulties in fitting and in interpretation additive models can be useful in the analysis of cohort studies

families of optimal oocs with lambda 2 we provide a new construction yielding one new and one known infinite family of optimal n w 2 optical orthogonal codes w isin 4 6 our construction relies on various techniques in finite projective spaces involving hyperovals in projective planes and singer groups

on conflict avoiding codes of length n 4m for three active users new improved upper and lower bounds on the maximum size of a symmetric or arbitrary conflict avoiding code of length n 4 m for three active users are proved furthermore direct constructions for optimal conflict avoiding codes of length n 4 m and m equiv 2 mod 4 for three active users are provided

optimal conflict avoiding codes of even length and weight 3 direct constructions for optimal conflict avoiding codes of length n equiv 4 pmod 8 and weight 3 are provided by bringing in a new concept called an extended odd sequence constructions for those odd sequences are also given in this paper as a consequence with previously known results the spectrum of the size of optimal conflict avoiding codes of even length and weight 3 is completely settled

optical orthogonal codes with unequal auto and cross correlation constraints an optical orthogonal code ooc is a collection of binary sequences with good auto and cross correlation properties they were defined by salehi and others as a means of obtaining code division multiple access on optical networks up to now all work on oocs have assumed that the constraint placed on the autocorrelation and that placed on the cross correlation are the same we consider codes for which the two constraints are not equal specifically we develop bounds on the size of such oocs and demonstrate constriction techniques for building them the results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross correlation constraint these results suggest that for a given performance requirement the optimal ooc may be one with unequal constraints this paper also views oocs with unequal auto and cross correlation constraints as constant weight unequal error protection uep codes with two levels of protection the bounds derived are interpreted from this viewpoint

new constructions of optimal cyclically permutable constant weight codes three new constructions for families of cyclic constant weight codes are presented all are asymptotically optimum in the sense that in each case as the length of the sequences within the family approaches infinity the ratio of family size to the maximum possible under the johnson upper bound approaches unity

toward a deterministic polynomial time algorithm with optimal additive query complexity in this paper we study two combinatorial search problems the coin weighing problem with a spring scale also known as the vector reconstructing problem using additive queries and the problem of reconstructing weighted graphs using additive queries suppose we are given n identical looking coins suppose that m out of the n coins are counterfeit and the rest are authentic assume that we are allowed to weigh subsets of coins with a spring scale it is known that the optimal number of weighings for identifying the counterfeit coins and their weights is at least w mlognlogm we give a deterministic polynomial time adaptive algorithm for identifying the counterfeit coins and their weights using o mlognlogm mloglogm weighings assuming that the weight of the counterfeit coins are greater than the weight of the authentic coins this algorithm is optimal when email protected n c l o g l o g n where c is any constant also our weighing complexity is within loglogm times the optimal complexity for all m to obtain this result our algorithm makes use of search matrices the divide and conquer approach and the guess and check approach when combining these methods with the technique introduced in h mazzawi 2008 20 we get a similar positive result for the problem of reconstructing a hidden weighted graph using additive queries

on the constructions of constant weight codes two methods of constructing binary constant weight codes from 1 codes over gf q and 2 constant weight codes over gf q are presented several classes of binary optimum constant weight codes are derived from these methods in general we show that binary optimum constant weight codes which achieve the johnson bound can be constructed from optimum codes over gf q which achieve the plotkin bound finally several classes of optimum constant weight codes over gf q are constructed

global stabilization of mimo minimum phase nonlinear systems without strict triangular conditions an extension of backstepping to a class of multivariable minimum phase nonlinear systems is proposed the systems are assumed to be in a special interlaced form which includes a lower triangular form as a special case the extension involves the recursive application of backstepping and augmentation

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

the standard h problem and the maximum principle the general linear case the classical relatively simple ideas of linear quadratic lq optimization are used in a time domain treatment of the standard h infty problem given the power of time domain analysis the problem can be solved in the general framework of linear time varying possibly infinite dimensional finite as well as infinite horizon systems under no structural restrictions such as block dimensions zero blocks in the d operator etc in the spirit of recent finite dimensional linear time invariant lti results the solution is given in terms of two coupled riccati equations it includes a criterion for suboptimality and a parametrization of all suboptimal compensators results pertinent to lti periodic and asymptotic systems are obtained as corollaries

empirical comparisons of proportional hazards and logistic regression models we compare parameter estimates from the proportional hazards model the cumulative logistic model and a new modified logistic model referred to as the person time logistic model with the use of simulated data sets and with the following quantities varied disease incidence risk factor strength length of follow up the proportion censored non proportional hazards and sample size parameter estimates from the person time logistic regression model closely approximated those from the cox model when the survival time distribution was close to exponential but could differ substantially in other situations we found parameter estimates from the cumulative logistic model similar to those from the cox and person time logistic models when the disease was rare the risk factor moderate and censoring rates similar across the covariates we also compare the models with analysis of a real data set that involves the relationship of age race sex blood pressure and smoking to subsequent mortality in this example the length of follow up among survivors varied from 5 to 14 years and the cox and person time logistic approaches gave nearly identical results the cumulative logistic results had somewhat larger p values but were substantively similar for all but one coefficient the age race interaction the latter difference reflects differential censoring rates by age race and sex

risk scores from logistic regression unbiased estimates of relative and attributable risk in epidemiology the risk of disease in terms of a set of covariates is often modelled by logistic regression the resulting linear predictor can be used to define the extent of risk between extremes and to calculate an attributable risk for the covariates taken together as is well known straightforward use of the linear predictor on the sample from which it was derived to obtain estimates the relative and attributable risk will be biased often seriously use of the jack knife technique is extended to produce asymptotically unbiased estimates of relative and attributable risks the asymptotic variances associated with these estimates are derived by using the formulae of conditional variances they are applied to the results of a case control study of stomach cancer

construction and applications of crt sequences protocol sequences are used for channel access in the collision channel without feedback each user accesses the channel according to a deterministic zero one pattern called the protocol sequence in order to minimize fluctuation of throughput due to delay offsets we want to construct protocol sequences whose pairwise hamming cross correlation is as close to a constant as possible in this paper we present a construction of protocol sequences which is based on the bijective mapping between one dimensional 1 d sequence and two dimensional 2 d arrays by the chinese remainder theorem crt in the application to the collision channel without feedback a worst case lower bound on system throughput is derived

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

multivariate piecewise exponential survival modeling in this article we develop a piecewise poisson regression method to analyze survival data from complex sample surveys involving cluster correlated differential selection probabilities and longitudinal responses to conveniently draw inference on absolute risks in time intervals that are prespecified by investigators extensive simulations evaluate the developed methods with extensions to multiple covariates under various complex sample designs including stratified sampling sampling with selection probability proportional to a measure of size pps and a multi stage cluster sampling we applied our methods to a study of mortality in men diagnosed with prostate cancer in the prostate lung colorectal and ovarian plco cancer screening trial to investigate whether a biomarker available from biospecimens collected near time of diagnosis stratifies subsequent risk of death poisson regression coefficients and absolute risks of mortality and the corresponding 95 confidence intervals for prespecified age intervals by biomarker levels are estimated we conclude with a brief discussion of the motivation methods and findings of the study

robust stabilization with positive real uncertainty beyond the small gain theory in many applications of feedback control phase information is available concerning the plant uncertainty for example lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions closed loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators in this paper the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real but otherwise unknown plant uncertainty these results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty one of the principal motivations for these results is to utilize phase information in guaranteeing robust stability in this these sense results go beyond the usual limitations the small gain theorem and quadratic lyapunov functions which may be conservative when phase information is available the results of this paper are based upon a riccati equation formulation of the positive real lemma and thus are in the spirit of recent riccati based approaches to bounded real h control

code sequences for frequency hopping multiple access systems a new code construction is given for slow frequency hopping multiple access channels the construction is based on the cyclic concatenation of special subcodes of two reed solomon codes

optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4 an optical orthogonal signature pattern code oospc finds application in transmitting 2 d images through multicore fiber in code division multiple access cdma communication systems observing a one to one correspondence between an oospc and a certain combinatorial subject called a packing design we present a construction of optimal oospcs with weight 4 and maximum collision parameter 2 which generalizes a well known kohler construction of optimal optical orthogonal codes ooc with weight 4 and maximum collision parameter 2 using this new construction enables one to obtain infinitely many optimal oospcs whose existence was previously unknown we prove that for a multiple n of 4 there exists no optimal oospc of size 6 n with weight 4 and maximum collision parameter 2 together with a report which shows a gap between optimal oocs and optimal oospcs when 6 and n are not coprime we also present a recursive construction of oospcs which are asymptotically optimal with respect to the johnson bound as a by product we obtain an asymptotically optimal m n 4 2 oospc for all positive integers m and n

on the design of synthetic case control studies a design is proposed for case control within cohort studies in this design controls are sampled without replacement from failure free members of the cohort at each distinct failure time upon selection a subject ceases to be eligible for control selection at later failure times also if a subject failing at time t had been selected as a control at t less than t then the matched controls at t are selected to have also been at risk at t in these circumstances correlation exists between score statistic contributions at t and t an estimator is developed for this correlation a small simulation study compares the design just described to other possible synthetic case control designs

improved semidefinite programming bound on sizes of codes let a n d respectively a n d w be the maximum possible number of codewords in a binary code respectively binary constant weight w code of length n and minimum hamming distance at least d by adding new linear constraints to schrijver s semidefinite programming bound which is obtained from block diagonalizing the terwilliger algebra of the hamming cube we obtain two new upper bounds on a n d namely a 18 8 71 and a 19 8 131 twenty three new upper bounds on a n d w for n 28 are also obtained by a similar way

goodness of fit of relative survival models additive regression models are preferred over multiplicative models in the analysis of relative survival data such preferences are mainly grounded in practical experience with mostly cancer registries data where the basic assumption of the additivity of hazards is more likely to be met also the interpretation of coefficients is more meaningful in additive than in multiplicative models nonetheless the question of goodness of fit of the assumed model must still be addressed and while there is an abundance of methods to check the goodness of fit of multiplicative models the respective arsenal for additive models is almost empty we propose here a variety of procedures for testing the null hypothesis of a good fit these are based on partial residuals defined similarly to schoenfeld residuals familiar for cox model diagnostics the tests have appropriate sizes under the null hypothesis and good power under different alternatives we investigate their performance through simulations and apply the methods to data from a study into survival of colon cancer patients

cyclic constant weight codes upper bounds and new optimal constructions in this paper we consider optimal q ary cyclic constant weight codes of length n minimum distance d and weight w briefly cyclic n d w q codes we introduce the pure and mixed difference method to present a combinatorial description for a cyclic n d w q code and then obtain some tight upper bounds on the sizes of optimal cyclic n d w q codes finally by using skolem type sequences we completely determine the sizes of optimal cyclic n d 3 3 codes with minimum distance 1 leq d leq 6

empirical evaluation of statistical models for counts or rates we consider methods for selecting the joint specification of the mean and variance functions in statistical models for rates or counts based on analyses of diagnosis specific hospital discharge rates in michigan we show that a poisson model with an extra variance component for the systematic variation is superior to several other probability models with regard to specification of the error structure further the deviance residual appears superior to the pearson residual the proper specification of such variation is crucial for many types of analyses such as identification of outliers and regression analyses designed to explain the systematic component of the variation

input output norms in general linear systems upper bounds on the induced norm of the input output operators in linear systems with l2 input and output signals are provided the main idea is to transform the original problem into a parametized set of indefinite lq optimization problems using the classical maximum principle the existence of solutions to the latter is equivalent to the solvability of a boundary value hamiltonian system or equivalenty of an indefinite riccati equation our time domain approach enables the treatment of a very general linear set up including time varying infinite dimensional finite and infinite horizon systems

on the use of covariates for rodent bioassay and screening experiments summary consider a three state compartmental model with an initial an absorbing and an intermediate state which may or may not be entered before absorption observable data are time to absorption and an indication of whether the intermediate state was entered but not the time of transition the transition rates characterizing the process are nonidentifiable without simplifying assumptions or additional information on the prevalence function defined as the time specific proportion of nonabsorbed individuals in the intermediate state our approach makes prevalence identifiable and easily estimable through the use of covariates combined with one or more random screens of the population the results are illustrated with pathology data from a rodent tumourigenicity experiment involving several random sacrifices

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

control sample size when cases are given in constant ratio stratum matched case control studies strata matched case control studies based on a given number of cases and k times as many controls are common we obtain a necessary and sufficient condition for there to exist a numerical solution for k with a desired level of a power we derive the maximum power of the cochran test which may be less than one when the number of cases is fixed we provide an approximate formula for the minimum number of cases required for a specified power there exists a numerical solution that is convergence of an iterative method for k if the number of cases given is greater than this minimum number and no such a solution otherwise we also show that the incremental gain in relative efficiency of the test with respect to k is diminished as k gets large

validity and efficiency of approximation methods for tied survival times in cox regression survival time studies sometimes do not yield distinct failure times several methods have been proposed to handle the resulting ties the goal of this paper is to compare these methods simulations were conducted in which failure times were generated for a two sample problem with an exponential hazard a constant hazard ratio and no censoring failure times were grouped to produce heavy moderate and light ties corresponding to a mean of 10 0 5 0 and 2 5 failures per interval cox proportional hazards models were fit using each of three approximations for handling ties with each interval size for sample sizes of n 25 50 250 and 500 in each group the breslow 1974 biometrics 30 89 99 approximation tends to underestimate the true beta while the kalbfleisch prentice 1973 biometrika 60 267 279 approximation tends to overestimate beta as the ties become heavier the bias of these approximations increases the efron 1977 journal of the american statistical association 72 557 565 approximation performs far better than the other two particularly with moderate or heavy ties even with n 25 in each group the bias is under 2 and for sample sizes larger than 50 per group it is less than 1 except for the heaviest ties in the smallest sample confidence interval coverage for all three estimators fell in the range of 94 96 however the tail probabilities were asymmetric with the breslow and kalbfleisch prentice formulas using the efron approximation they were closer to the nominal 2 5 although the breslow approximation is the default in many standard software packages the efron method for handling ties is to be preferred particularly when the sample size is small either from the outset or due to heavy censoring

on the reduction of certain frequency shaped linear quadratic dissipative design problems to an h sub spl infin formulation this paper concerns a concept of frequency based quadratic dissipativity and its reduction to an equivalent h sub spl infin or spl mu condition the paper is motivated by the observation that a strictly proper system cannot be strictly passive hence results on the synthesis of positive real systems using the cayley transform directly cannot be applied in most physical situations

constructions of protocol sequences for multiple access collision channel without feedback constructions of protocol sequences for multiple access collision channel without feedback are given these constructions are the extensions of those described by a gyorfi and massey see ibid vol 38 p 940 may 1992 if the basic code in their constructions a reed solomon code is replaced by a bch code then the resulting protocol sequences have the feature that for a given sum rate the ratio of the total user population to the block length becomes much larger

bias in indirectly adjusted comparisons due to taking the total study population as the reference group it is well known that comparisons of indirectly adjusted statistics such as standardized morbidity ratios smrs can be biased when the joint effect of the study exposure and thecovariates is not multiplicative this paper describes a related bias in smr comparisons one that can arise if the total study population is used as the referent this bias can occur even if the exposure covariate effects are multiplicative

asymptotic theory for nested case control sampling in the cox regression model by providing a probabilistic model for nested case control sampling in epidemiologic cohort studies consistency and asymptotic normality of the maximum partial likelihood estimator of regression parameters in a cox proportional hazards model can be derived using process and martingale theory as in andersen and gill a general expression for the asymptotic variance is given and used to calculate asymptotic relative efficiencies relative to the full cohort variance in some important special cases

synthesis of positive real multivariable feedback systems this is a tutorial paper describing the application of infinity norm optimal control theory to the synthesis of sector bounded and positive real multivariable feedback systems the paper gives a concise treatment of the practical aspects of the theory describing how it has been implemented via state space oriented computer algorithms included is a concise summary of the state space approach to infinity norm control developed by doyle and by safonov and verma based on the hankel model reduction theory and incorporating the multivariable hankel results of glover

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

a general upper bound on the size of constant weight conflict avoiding codes conflict avoiding codes are used in the multiple access collision channel without feedback the number of codewords in a conflict avoiding code is the number of potential users that can be supported in the system in this paper a new upper bound on the size of constant weight conflict avoiding codes is proved this upper bound is general in the sense that it is applicable to all code lengths and all hamming weights several existing constructions for conflict avoiding codes which are known to be optimal for hamming weights equal to four and five are shown to be optimal for all hamming weights in general

multiplicative models and cohort analysis abstract three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age calendar year specific death rates the first method which assumes that the baseline rates are known from national vital statistics is a multiple regression analysis of the standardized mortality ratio the second method is a variant of cox s proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters the third method consists of case control sampling from the risk sets formed in the course of applying cox s model it requires substantially less computation than do the other two in illustrative analysis of respiratory cancer deaths among a cohort of smelter workers all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure the discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis and on practica

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

how an erdos renyi type search approach gives an explicit code construction of rate 1 for random access with multiplicity feedback pippenger 1981 showed in a probabilistic way that the capacity of a collision channel with multiplicity feedback is one in this correspondence using an erdos renyi type search strategy we settle a long standing open problem by giving a constructive proof of this result moreover we prove that two different capacity definitions are equivalent thereby solving a problem posed by tsybakov 1985

maximum distance separable multilevel codes corresp a class of t error correcting pseudocyclic multilevel codes is introduced these are maximum distance separable random error correcting codes with qm symbols where q is a prime number the construction of seven level codes is presented as an example

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

perfect constant weight codes in his pioneering work from 1973 delsarte conjectured that there are no nontrivial perfect codes in the johnson scheme many attempts were made during the years which followed to prove delsarte s conjecture but only partial results have been obtained we survey all these attempts and prove some new results having the same flavor we also present a new method taking a different approach which we hope can lead to the settling of this conjecture we show how this new method rules out sets of parameters as well as specific given parameters

data analytic methods for matched case control studies the recent introduction of complex multivariate statistical models in matched case control studies is a mixed blessing their use can lead to a better understanding of the way in which many variables contribute to the risk of disease on the other hand these powerful methods can obscure salient features in the data that might have been detected by other less sophisticated methods this shortcoming is due to a lack of support methodology for the routine use of these models satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model goodness of fit must be examined if inferences are to be trusted this paper is concerned with the analysis of matched case control studies with logistic models analogies of these models to linear regression models are emphasized in particular basic concepts such as analysis of variance multiple correlation coefficient one degree of freedom tests and residual analysis are discussed the fairly new field of regression diagnostics is also introduced all procedures are illustrated on a study of bladder cancer in males

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

constructions of binary constant weight cyclic codes and cyclically permutable codes a general theorem is proved showing how to obtain a constant weight binary cyclic code from a p ary linear cyclic code where p is a prime by using a representation of gf p as cyclic shifts of a binary p tuple based on this theorem constructions are given for four classes of binary constant weight codes the first two classes are shown to achieve the johnson upper bound on minimum distance asymptotically for long block lengths the other two classes are shown similarly to meet asymptotically the low rate plotkin upper bound on minimum distance a simple method is given for selecting virtually the maximum number of cyclically distinct codewords with full cyclic order from reed solomon codes and from berlekamp justesen maximum distance separable codes two correspondingly optimum classes of constant weight cyclically permutable codes are constructed it is shown that cyclically permutable codes provide a natural solution to the problem of constructing protocol sequence sets for the m active out of t users collision channel without feedback

exact tests of goodness of fit of log linear models for rates we propose metropolis hastings sampling methods for estimating the exact conditional p value for tests of goodness of fit of log linear models for mortality rates and standardized mortality ratios we focus on two way tables where the required conditional distribution is a multivariate noncentral hypergeometric distribution with known noncentrality parameter two examples are presented a 2 3 table where the exact results obtained by enumeration are available for comparison and a 9 7 table where monte carlo methods provide the only feasible approach for exact inference

on the fitting of generalized linear models with nonnegativity parameter constraints summary we consider the problem of finding maximum likelihood estimates of a generalized linear model when some or all of the regression parameters are constrained to be nonnegative the kuhn tucker conditions of nonlinear programming can be used to characterize the solution of this constrained estimation problem when the maximum likelihood estimates exist and are unique for the case of a generalized linear model with nonnegativity parameter constraints the kuhn tucker conditions are derived and utilized to provide a stopping rule for search algorithms for the constrained maximum likelihood estimates two examples are discussed

extended reed solomon codes for optical cdma in this paper the extended reed solomon codes are modified to construct a new family of 2 d codes for asynchronous optical code division multiple access o cdma in addition of having expanded and asymptotically optimal cardinality these 2 d asynchronous optical codes can be partitioned into multiple tree structures of code subsets in which code cardinality is a function of the periodic cross correlation value assigned to the subset the performance of these 2 d optical codes is analyzed and compared with that of the multilevel prime codes our results show that the unique partition property of the new optical codes supports a trade off between code cardinality and performance for meeting different system requirements such as user capacity and throughput in addition the multiple tree structures of the new codes potentially support applications that require rapid switching of many codewords such as in o cdma network gateway or in strategic environments where code obscurity is essential

simple parametric and nonparametric models for excess and relative mortality this paper studies two classes of hazard rate based models for the mortality in a group of individuals taking normal life expectancy into account in a multiplicative hazard model the estimate for the relative mortality generalises the standardised mortality ratio and the adequacy of a model with constant relative mortality can be tested using a type of total time on test statistic in an additive hazard model continuous time generalisations of a corrected survival curve and a normal survival curve are obtained and the adequacy of a model with constant excess mortality can again be tested using a type of total time on test statistic a model including both the multiplicative hazard model and the additive hazard model is briefly considered the use of the models is illustrated on a set of data concerning survival after operation for malignant melanoma

weight calibration to improve the efficiency of pure risk estimates from case control samples nested in a cohort cohort studies provide information on relative hazards and pure risks of disease for rare outcomes large cohorts are needed to have sufficient numbers of events making it costly to obtain covariate information on all cohort members we focus on nested case control designs that are used to estimate relative hazard in the cox regression model in 1997 langholz and borgan showed that pure risk can also be estimated from nested case control data however these approaches do not take advantage of some covariates that may be available on all cohort members researchers have used weight calibration to increase the efficiency of relative hazard estimates from case cohort studies and nested cased control studies our objective is to extend weight calibration approaches to nested case control designs to improve precision of estimates of relative hazards and pure risks we show that calibrating sample weights additionally against follow up times multiplied by relative hazards during the risk projection period improves estimates of pure risk efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks we develop explicit variance formulas for the weight calibrated estimates simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality examples are provided using data from the american association of retired persons diet and health cohort study

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

recursive constructions of detecting matrices for multiuser coding a unifying approach detecting matrices are a class of combinatorial objects originated from the coin weighing problem of soderberg and shapiro in the early 1960s in this paper various known recursive construction techniques for binary bipolar and ternary detecting matrices are reexamined in a unifying framework new general recursive constructions of detecting matrices which include previous recursive constructions as special cases are derived such matrices find applications in multiuser coding since they are equivalent to a certain class of uniquely decodable multiuser codes for the binary adder channel interestingly it is found that among the three kinds of detecting matrices ternary detecting matrices are of fundamental significance from the combinatorial theoretic as well as from the multiuser coding application point of view

nonparametric estimation of relative mortality from nested case control studies andersen et al 1985 biometrics 41 921 932 gave an estimator of the cumulative relative mortality comparing rates of death in an epidemiologic cohort to an external population as a function of time when covariate information is available on all cohort members we present an analogous estimator when covariate information is known only on a nested case control sample counting process techniques are used to show that this estimator is almost unbiased and an estimator of its variance is derived estimators of the relative mortality function using kernel smoothing methods and the average relative mortality over grouped time intervals are also presented the methods are illustrated by comparing rates of lung cancer mortality in a cohort of montana smelter workers to that in the united states population

survival analysis of backward recurrence times abstract many surveys include questions that attempt to measure the time of the most recent occurrence of some event for example last visit to a physician although it is tempting to apply survival failure time methods to such data the conditions under which such applications are appropriate have not been apparent in this article it is shown that standard methods may be applied when the data arise from certain well known stochastic processes special procedures may be necessary if the models include duration dependence however the methods are illustrated by the estimation of regression models for data on residential mobility