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

global stability of an hiv 1 infection model with saturation infection and intracellular delay in this paper an hiv 1 infection model with a saturation infection rate and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated by analyzing the characteristic equations the local stability of an infection free equilibrium and a chronic infection equilibrium of the model is established by using suitable lyapunov functionals and the lasalle invariant principle it is proved that if the basic reproduction ratio is less than unity the infection free equilibrium is globally asymptotically stable if the basic reproduction ratio is greater than unity the chronic infection equilibrium is globally asymptotically stable

threshold dynamics of a delayed nonlocal reaction diffusion hiv infection model with both cell free and cell to cell transmissions abstract in this paper we derive and analyze an hiv infection model containing a fixed latent period and both cell free and cell to cell transmissions the model is described by a spatially non local reaction diffusion system with the zero flux condition on the boundary we first show that the model admits global solutions and possesses a global attractor following the definition of the next infection operator we obtain the expression of the basic reproduction number 0 which is shown as a threshold parameter for the model dynamics our results indicate that the clearance persistence of hiv is governed by the sign of 0 1 in particular an explicit formula of 0 is given in the homogeneous case

reversed version of a generalized sharp holder s inequality and its applications in this paper we give a reversed version of a generalized sharp holder s inequality which is due to wu the results are then used to improve beckenbach s inequality and minkowski s inequality moreover as an application in information theory we present a refinement of singh s inequality which is one generalized shannon s inequality

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

global stability for a virus dynamics model with nonlinear incidence of infection and removal global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct lyapunov method where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear in the case where the functional quotient between the force of infection and the removal rate of the virus is a nonincreasing function of the virus concentration the existence of a threshold parameter i e the basic reproduction number or basic reproductive ratio is established and the global stability of the equilibria is discussed moreover in the absence of the above mentioned monotonicity property estimations for the sizes of the domains of attraction are given biological significance of the results and possible extensions of the model are also discussed

on some matrix reverse cauchy schwarz and holder inequalities abstract in this paper we present some eigenvalue inequalities related to the reverse holder inequality involving positive linear maps geometric means and doubly concave functions several relevant inequalities are considered as well

more accurate operator means inequalities abstract our main target in this paper is to present new sharp bounds for inequalities that result when weighted operator means are filtered through positive linear maps and operator monotone functions as an application we prove a refined reverse of the celebrated golden thompson inequality furthermore we show how these inequalities can be squared

age dependency in host vector models the global analysis in this paper we introduce and analyze two structured models for the transmission of a vector borne infectious disease the first of these models assumes that the level of contagiousness and the rate of removal recovery of infected hosts depends on the infection age in the second model the hosts population is structured with respect to the physical age of the hosts and the susceptibility of the hosts is assumed to be age dependent for these models the threshold parameter for the existence of a positive endemic equilibrium state is determined and the global asymptotic stability of the equilibrium states are established by the lyapunov s direct method

lyapunov functions and global stability for age structured hiv infection model we study the basic age structured population model describing the hiv infection process which is defined by pdes the model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age by using the direct lyapunov method and constructing suitable lyapunov functions dynamical properties of the age structured model without or with drug treatment are established the results show that the global asymptotic stability of the infection free steady state and the infected steady state depends only on the basic reproductive number determined by the burst size further we establish mathematically that the typical ode and dde delay differential equation models of hiv infection are equivalent to two special cases of the above pde models

asymptotic properties of a hiv 1 infection model with time delay based on some important biological meanings a class of more general hiv 1 infection models with time delay is proposed in the paper in the hiv 1 infection model time delay is used to describe the time between infection of uninfected target cells and the emission of viral particles on a cellular level as proposed by herz et al a v m herz s bonhoeffer r m anderson r m may m a nowak viral dynamics in vivo limitations on estimates of intracellular delay and virus decay proc natl acad sci usa 93 1996 7247 7251 then the effect of time delay on stability of the equilibria of the hiv 1 infection model has been studied and sufficient criteria for local asymptotic stability of the infected equilibrium and global asymptotic stability of the viral free equilibrium are given

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

matrix versions of some classical inequalities abstract some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals in particular we show matrix versions of chebyshev and kantorovich type inequalities the matrix approach may also provide simplified proofs and new results for classical inequalities for instance we show a link between cassel s inequality and the basic rearrangement inequality for sequences of hardy littlewood polya and we state a reverse inequality to the hardy littlewood polya inequality in which matrix technics are essential

a matrix reverse cauchy schwarz inequality abstract the matrix geometric mean is concave we complete this important fact with a reverse result this follows from an interesting non commutative extension of a classical reverse cauchy schwarz inequality cassel 1951 our investigation also leads to state a reverse result to von neuman s trace inequality

a difference counterpart to a matrix holder inequality abstract we point out a sharp reverse cauchy schwarz holder matrix inequality the cauchy schwarz version involves the usual matrix geometric mean let a i and b i be positive definite matrices such that 0 ma i b i ma i for some scalars 0 m m and i 1 2 n then i 1 n a i i 1 n b i i 1 n a i b i m m 2 4 m m i 1 n a i where the matrix geometric mean of positive definite a and b is defined by a b a 1 2 a 1 2 ba 1 2 1 2 a 1 2

on an operator kantorovich inequality for positive linear maps abstract we improve the operator kantorovich inequality as follows let a be a positive operator on a hilbert space with 0 m a m then for every unital positive linear map a 1 2 m m 2 4 m m 2 a 2 as a consequence a 1 a a a 1 m m 2 2 m m

new inequalities for the generalized karcher mean abstract recently palfia introduced a generalized karcher mean as a solution of an operator equation in this article we present several relations for this new mean in particular we investigate the behavior of this generalized mean when filtered through operator monotone functions and positive linear maps revealing its information monotonicity

delay versus age of infection global stability abstract we consider an sir model of disease transmission which has been formulated with delay in order to give a fixed duration of infectiousness a lyapunov functional that has worked for similar models does not work here instead the model is shown to be a consequence of an age of infection model for which the same class of lyapunov functionals has worked resolving the global stability

combining the advantages of one sided and two sided test procedures for comparing several treatment effects abstract we consider the one way layout for comparing k treatment effects i 1 i k hayter earlier proposed a one sided studentized range test osrt for testing the null hypothesis h o 1 2 k against the simple ordered alternative ha 1 2 k with at least one strict inequality the osrt gives a set of simultaneous confidence intervals for all ordered pairwise differences j i i 0 but provides two sided finite confidence intervals if the sample averages are all far apart

squaring operator polya szego and diaz metcalf type inequalities abstract we square operator polya szego and diaz metcalf type inequalities as follows if operator inequalities 0 m 1 2 a m 1 2 and 0 m 2 2 b m 2 2 hold for some positive real numbers m 1 m 1 and m 2 m 2 then for every unital positive linear map the following inequalities hold a b 2 m 1 m 2 m 1 m 2 2 m 1 m 2 m 1 m 2 4 a b 2 and m 2 m 2 m 1 m 1 a b 2 m 1 m 1 m 2 2 m 2 2 m 2 m 2 m 1 2 m 1 2 2 8 m 2 m 1 m 1 m 2 m 1 2 m 1 2 m 2 m 2 2 a b 2

quantum reverse hypercontractivity we develop reverse versions of hypercontractive inequalities for quantum channels by generalizing classical techniques we prove a reverse hypercontractive inequality for tensor products of qubit depolarizing channels we apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces and to prove bounds on a quantum generalization of non interactive correlation distillation

generalized matrix version of reverse holder inequality abstract a generalized matrix version of reverse cauchy schwarz holder inequality is proved this includes the recent results proved by bourin fujii lee niezgoda and seo

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

group testing for case identification with correlated responses this article examines group testing procedures where units within a group or pool may be correlated the expected number of tests per unit i e efficiency of hierarchical and matrix based procedures is derived based on a class of models of exchangeable binary random variables the effect on efficiency of the arrangement of correlated units within pools is then examined in general when correlated units are arranged in the same pool the expected number of tests per unit decreases sometimes substantially relative to arrangements that ignore information about correlation

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

global dynamics for a class of age infection hiv models with nonlinear infection rate abstract in this paper we study the global stability of a class of hiv viral infection models with continuous age structure using the direct lyapunov method in each of the cases where the incidence rates are given by nonlinear infection rate f t g v holling type ii functional response and crowley martin functional response we define the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not we give a rigorous mathematical analysis on technical materials and necessary arguments including relative compactness of the orbit and uniform persistence of system by reformulating the system as a system of volterra integral equations we further investigate global behaviors of hiv viral infection models with holling type ii functional response and crowley martin functional response through numerical simulations

use of binomial group testing in tests of hypotheses for classification or quantitative covariables summary in group testing the test unit consists of a group of individuals if the group test is positive then one or more individuals in the group are assumed to be positive a group observation in binomial group testing can be say the test result positive or negative for a pool of blood samples that come from several different individuals it has been shown that when the proportion p of infected individuals is low group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected we extend the potential applications of group testing to hypothesis testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable asymptotic relative efficiencies ares of tests based on group testing versus the usual individual testing are obtained the pitman are strongly favors group testing in many cases small sample results from simulation studies are given and are consistent with the large sample asymptotic findings we illustrate the potential advantages of group testing in hypothesis testing using hiv 1 seroprevalence data

generalized polya szego type inequalities for some non commutative geometric means in this paper we shall show generalized polya szego type inequalities of n positive invertible operators on a hilbert space for any integer n 3 in terms of the following two typical non commutative geometric means that is one is the higher order weighted geometric mean due to lawson lim which is an extension of the ando li mathias geometric mean and the other is the weighted chaotic geometric mean among others the specht ratio plays an important role in our discussion which is the upper bound of a ratio type reverse of the weighted arithmetic geometric mean inequality

a matrix reverse holder inequality abstract a matrix reverse holder inequality is given this result is a counterpart to the concavity property of matrix weighted geometric means it extends a scalar inequality due to gheorghiu and contains several kantorovich type inequalities

group testing with blockers and synergism discovery and development of a new drug can cost hundreds of millions of dollars pharmaceutical companies have used group testing methodology routinely as one of the efficient high throughput screening techniques to search for lead compounds among collections of hundreds of thousands of chemical compounds the lead compounds can be modified to produce new and effective molecules which eventually may lead to new drugs this article develops models and estimation procedures to obtain quantitative information from data in such applications it investigates group testing procedures and studies cost efficiency when the standard assumption adopted by dorfman that tested items act independently of one another is violated the investigation is focused on but not limited to the square array pooling method and the methodologies developed are illustrated through simulations and a drug discovery dataset from glaxo wellcome inc