optimality of group testing in the presence of misclassification several optimality properties of dorfman s 1943 group testing procedure are derived for estimation of the prevalence of a rare disease whose status is classified with error exact ranges of disease prevalence are obtained for which group testing provides more efficient estimation when group size increases

a generalization of the schur siegel smyth trace problem abstract let be a totally positive algebraic integer and define its absolute trace to be tr deg the trace of divided by the degree of elementary considerations show that the absolute trace is always at least one while it is plausible that for any 0 the absolute trace is at least 2 with only finitely many exceptions this is known as the schur siegel smyth trace problem our aim in this paper is to show that the schur siegel smyth trace problem can be considered as a special case of a more general problem

rate of convergence of basic multivariate neural network operators to the unit this chapter deals with the determination of the rate of convergence to the unit of some multivariate neural network operators namely the normalized bell and squashing type operators

estimating ordered binomial proportions with the use of group testing summary this paper considers group testing when the probability of response is increasing across the levels of an observed covariate we illustrate how previously known results in order restricted inference can be extended to situations wherein data are collected according to a group testing protocol and we derive maximum likelihood estimators for proportions under the increasing order restriction and group testing model finally we show how the use of group testing can dramatically reduce the bias and mean squared error of isotonic regression estimators obtained from one at atime testing these proposed methods are illustrated using data from an observational hiv study conducted in houston texas

rate of convergence of basic neural network operators to the unit univariate case this chapter deals with the determination of the rate of convergence to the unit of some neural network operators namely the normalized bell and squashing type operators

on integer chebyshev polynomials we are concerned with the problem of minimizing the supremum norm on o 1 of a nonzero polynomial of degree at most n with integer coefficients we use the structure of such polynomials to derive an efficient algorithm for computing them we give a table of these polynomials for degree up to 75 and use a value from this table to answer an open problem due to p borwein and t erdelyi and improve a lower bound due to flammang et al

on the linear independence measure of logarithms of rational numbers in this paper we give a general theorem on the linear independence measure of logarithms of rational numbers and in particular the linear independence measure of 1 log 2 log 3 log 5 and of 1 log 2 log 3 log 5 log 7 we also give a method to search for polynomials of smallest norm on a real interval a b which may be suitable for computing or improving the linear independence measure of logarithms of rational numbers

using group testing to estimate a proportion and to test the binomial model group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion p of defectives is small it can also be used to estimate p often substantially reducing the mean squared error mse of p and cost per unit information group testing is useful for larger p in the estimation problem than in the classification problem but for larger p more care must be taken in choosing the group size k k being too large not only increases mse p but adversely affects the robustness of p to both errors in testing misclassification and errors in the assumed binomial model procedures that retest units from defective groups if even feasible are shown to reduce cost per unit information very little in the estimation problem but can provide useful information for testing the model methods are given for using data from tests of unequal sized groups to estimate p and for testing the validity of the binomial model

the integer chebyshev problem the main problem of this chapter is to find a polynomial in z n of minimal supremum norm on an interval this is p1 and it is of a slightly different flavour than most of the other problems in this book in that there is no restriction on the size of the coefficients we now state p1 with greater precision

the trace of totally positive algebraic integers for all totally positive algebraic numbers except a finite number of explicit exceptions the following inequality holds 1 d 1 d max 1 780022 1 66 1 where d is the degree of a and 0 1 d its conjugates this improves previous results of smyth flammang and rhin

algebraic integers whose conjugates all lie in an ellipse we find all 15909 algebraic integers whose conjugates all lie in an ellipse with two of them nonreal while the others lie in the real interval 1 2 this problem has applications to finding certain subgroups of sl 2 c we use explicit auxiliary functions related to the generalized integer transfinite diameter of compact subsets of c this gives good bounds for the coefficients of the minimal polynomial of a

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

the errors of simultaneous approximation of multivariate functions by neural networks there have been many studies on the simultaneous approximation capability of feed forward neural networks fnns most of these however are only concerned with the density or feasibility of performing simultaneous approximations this paper considers the simultaneous approximation of algebraic polynomials employing taylor expansion and an algebraic constructive approach to construct a class of fnns which realize the simultaneous approximation of any smooth multivariate function and all of its derivatives we also present an upper bound on the approximation accuracy of the fnns expressed in terms of the modulus of continuity of the functions to be approximated

trace of totally positive algebraic integers and integer transfinite diameter the diameter of a totally real algebraic integer of degree d with conjugates 1 2 d is diam d 1 for all positive integers k and n diam 2 cos 2k n is less than 4 r m robinson has computed modulo integer translations all the other totally real algebraic integers with diam 4 for d 8 we have done the computations for all d 15 we use a large family of explicit auxiliary functions related to generalized integer transfinite diameter of real intervals they give good bounds for the coefficients of the minimal polynomial of for d 15 we prove a recent conjecture of capparelli et al mathematics subject classification 2000 primary 11c08 11y40

integer transfinite diameter and polynomials with small mahler measure in this work we show how suitable generalizations of the integer transfinite diameter of some compact sets in c give very good bounds for coefficients of polynomials with small mahler measure by this way we give the list of all monic irreducible primitive polynomials of z x of degree at most 36 with mahler measure less than 1 324 and of degree 38 and 40 with mahler measure less than 1 31

a trace bound for positive definite connected integer symmetric matrices abstract let a be a connected integer symmetric matrix i e a a i j m n z for some n a a t and the underlying graph vertices corresponding to rows with vertex i joined to vertex j if a i j 0 is connected we show that if all the eigenvalues of a are strictly positive then tr a 2 n 1 there are two striking corollaries first the analogue of the schur siegel smyth trace problem is solved for characteristic polynomials of connected integer symmetric matrices second we find new examples of totally real separable irreducible monic integer polynomials that are not minimal polynomials of integer symmetric matrices

on the absolute mahler measure of polynomials having all zeros in a sector ii kklet be an algebraic integer of degree d not 0 or a root of unity all of whose conjugates i are confined to a sector arg z in the paper on the absolute mahler measure of polynomials having all zeros in a sector g rhin and c smyth compute the greatest lower bound c of the absolute mahler measure d i 1 max 1 i 1 d of for belonging to nine subintervals of 0 2 3 in this paper we improve the result to thirteen subintervals of 0 and extend some existing subintervals

robustness of group testing in the estimation of proportions in binomial group testing unlike one at a time testing the test unit consists of a group of individuals and each group is declared to be defective or nondefective a defective group is one that is presumed to include one or more defective e g infected positive individuals and a nondefective group to contain only nondefective individuals the usual binomial model considers the individuals being grouped as independent and identically distributed bernoulli random variables under the binomial model and presuming that groups are tested and classified without error it has been shown that when the proportion of defective individuals is low group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives we discuss the robustness of group testing for estimating proportions when the underlying assumptions of i no testing errors and ii independent individuals are violated to evaluate the effect of these model violations two dilution effect models and a serial correlation model are considered group testing proved to be quite robust to serial correlation in the presence of a dilution effect smaller group sizes should be used but most of the benefits of group testing can still be realized

a two stage adaptive group testing procedure for estimating small proportions abstract a method for adaptively estimating a proportion p using group testing procedures is presented and analyzed with emphasis placed on a two stage procedure this estimator is compared to the usual group testing estimator via asymptotic and small sample relative efficiency the adaptive estimator is generally recommended with the restriction that adaptations i e adjustments of group size are based on at least 10 measurements responses but if one is confident that one has a very good a priori estimate of p then the usual estimator is recommended monte carlo simulations show that a normal approximation is adequate for generating confidence intervals with confidence coefficients as high as 95

on the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease application to hiv screening summary when screening for a rare disease the large number of expected false positives makes it difficult to obtain a positive estimate of prevalence using current screening methodology pooled testing not only reduces the probability of this occurring but also improves the accuracy of the estimator these findings are illustrated by screening for the human immunodeficiency virus

group testing regression models with dilution submodels group testing where specimens are tested initially in pools is widely used to screen individuals for sexually transmitted diseases however a common problem encountered in practice is that group testing can increase the number of false negative test results this occurs primarily when positive individual specimens within a pool are diluted by negative ones resulting in positive pools testing negatively if the goal is to estimate a population level regression model relating individual disease status to observed covariates severe bias can result if an adjustment for dilution is not made recognizing this as a critical issue recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution in this paper we have the same overall goal but take a different approach we augment existing group testing regression models that assume no dilution with a parametric dilution submodel for pool level sensitivity and estimate all parameters using maximum likelihood an advantage of our approach is that it does not rely on external biomarker test data which may not be available in surveillance studies furthermore unlike previous approaches our framework allows one to formally test whether dilution is present based on the observed group testing data we use simulation to illustrate the performance of our estimation and inference methods and we apply these methods to 2 infectious disease data sets

computing totally positive algebraic integers of small trace we construct minimal polynomials of totally positive algebraic integers of small absolute trace by consideration of their reductions modulo auxiliary polynomials many new examples of such polynomials of minimal absolute trace for given degree are found the computations are pushed to degrees that previously were unattainable and one consequence is that the new examples form the majority of all those known as an application we produce a new bound for the schur siegel smyth trace problem

multivariate hyperbolic tangent neural network approximation here we study the multivariate quantitative approximation of real and complex valued continuous multivariate functions on a box or r n n n by the multivariate quasi interpolation hyperbolic tangent neural network operators this approximation is derived by establishing multidimensional jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives our multivariate operators are defined by using a multidimensional density function induced by the hyperbolic tangent function the approximations are pointwise and uniform the related feed forward neural network is with one hidden layer

estimating the mean of an increasing stochastic process at a censored stopping time abstract data often come in the form of a longitudinal series say n whose observation has been stopped either by a terminal event u e g death or censoring event c e g lost to follow up when n is not deterministic it is generally not possible to use standard survival analysis tools e g the kaplan meier estimator to consistently estimate functionals of the distribution of n u because of induced informative censoring various seemingly unrelated estimators recently have been proposed to handle this difficulty within the context of specific problems ranging from the analysis of quality adjusted survival data to recurrent event data to lifetime medical cost data in this article i consider a general framework containing each of these specific examples as a special case propose a class of estimators for the mean of the stopped longitudinal process and establish the asymptotic properties of this class of estimators connections between the aforementioned estimators are established