two parameter quantum affine algebra of type g2 1 drinfeld realization and vertex representation in this paper we define the two parameter quantum affine algebra for type g2 1 and give the r s drinfeld realization of ur s g2 1 as well as establish and prove its drinfeld isomorphism we construct and verify explicitly the level one vertex representation of two parameter quantum affine algebra ur s g2 1 which also supports an evidence in nontwisted type g2 1 for the uniform defining approach via the two parameter invariant generating functions proposed in hu and zhang generating functions with invariance and vertex representations of two parameter quantum affine algebras ur s g simply laced cases e print arxiv 1401 4925

drinfeld double of deformed quantum algebras abstract we provide a deformation f of lusztig algebra f various quantum algebras in literatures including half parts of two parameter quantum algebras quantum superalgebras and multi parameter quantum algebras superalgebras are all specializations of f moreover f is isomorphic to lusztig algebra f up to a twist as a consequence half parts of those quantum algebras are isomorphic to lusztig algebra f over a big enough ground field up to certain twists we further construct the entire algebra u by drinfeld double construction as special cases above quantum algebras all admit a drinfeld double construction under certain assumptions

nonparametric regression analysis for group testing data group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of for example blood urine or water instead of testing the sample of each individual the method involves pooling samples of groups of several individuals and testing those pooled samples we construct a nonparametric procedure for estimating the conditional probability of contamination given an explanatory variable when the observations are pooled data of this type we investigate asymptotic theoretical properties of the estimator and establish its consistency the procedure requires selecting an important smoothing parameter and we suggest a way to do this automatically from the data we illustrate the numerical performance of the method on some simulated examples and on data from the national health and nutrition examination survey we discuss extensions of the procedure to cases where the test is im

computation of 3 d velocity fields from 3 d cine ct images of a human heart a method of computing the three dimensional 3 d velocity field from 3 d cine computer tomographs cts of a beating heart is proposed using continuum theory the authors develop two constraints on the 3 d velocity field generated by a beating heart with these constraints the computation of the 3 d velocity field is formulated as an optimization problem and a solution to the optimization problem is developed using the euler lagrange method the solution is then discretized for computer implementation the authors present the results for both simulated images and clinical cine ct images of a beating heart

second order approximation to the risk of a sequential procedure given x 1 x 2 cdots i i d with mean mu and variance sigma 2 suppose that at stage n one wishes to estimate mu by the sample mean bar x n subject to the loss function l n a bar x n mu 2 n a 0 if sigma is known the optimal fixed sample size n 0 approx a 1 2 sigma can be used with corresponding risk r n 0 but if sigma is unknown there is no fixed sample size procedure that will achieve the risk r n 0 for the sequential estimation procedure with stopping rule t inf n geq n a n 1 sum n 1 x i bar x n 2 leq a 1 n 2 the second order approximation of woodroofe 1977 to the risk r t for normal x i is extended to the distribution free case specifically if the x i have finite moments of order greater than eight and are non lattice under certain conditions on the delay n a it is shown that the regret r t r n 0 c o 1 as a rightarrow infty where c depends on the first four moments of the distribution of the x i for the lattice case bounds of the form c 1 o 1 leq r t r n 0 leq c 2 o 1 are obtained where the c j are c pm 3 it follows from these approximations that the regret can take arbitrarily large negative values as the distribution of the x i varies in contrast to previous results for normal and gamma cases

sequentially deciding between two experiments for estimating a common success probability abstract to estimate a success probability p two experiments are available individual bernoulli p trials or the product of individual bernoulli p trials this problem has its roots in reliability where either single components can be tested or a system of identical components can be tested a total of n experiments can be performed and the problem is to sequentially select some combination allocation of these two experiments along with an estimator of p to achieve low mean squared error mse of the final estimate this scenario is similar to that of the better known group testing problem but here the goal is to estimate failure rates rather than to identify defective units the problem also arises in epidemiological applications such as estimating disease prevalence information maximization considerations and analysis of the asymptotic mse of several estimators lead to the following adaptive procedure use the maximum likelihood estimator mle to estimate p and if this estimator is b

yetter drinfeld modules under cocycle twists abstract we give an explicit formula for the correspondence between simple yetter drinfeld modules for certain finite dimensional pointed hopf algebras h and those for cocycle twists h of h this implies an equivalence between modules for their drinfeld doubles to illustrate our results we consider the restricted two parameter quantum groups u r s sl n under conditions on the parameters guaranteeing that u r s sl n is a drinfeld double of its borel subalgebra we determine explicit correspondences between u r s sl n modules for different values of r and s and provide examples where no such correspondence can exist our examples were obtained via the computer algebra system singular plural

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

two parameter twisted quantum affine algebras we establish drinfeld realization for the two parameter twisted quantum affine algebras using a new method the hopf algebra structure for drinfeld generators is given for both untwisted and twisted two parameter quantum affine algebras which include the quantum affine algebras as special cases

new approaches to nonparametric and semiparametric regression for univariate and multivariate group testing data summary we consider non and semi parametric estimation of a conditional probability curve in the case of group testing data where the individuals are pooled randomly into groups and only the pooled data are available we derive a nonparametric weighted estimator 15 that has optimality properties accounting for group sizes and show how to extend it to multivariate settings including the partially linear model in the group testing context it is natural to assume that the probability curve depends on the covariates only through a linear combination of them motivated by this we develop a nonparametric estimator based on the single index model we study theoretical properties of the sug 20 gested estimators and derive data driven procedures practical properties of the methods are demonstrated via real and simulated examples and shown to have smaller median integrated square error than existing competitors

determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast ct cardiac images a method of computing the velocity field and pressure distribution from a sequence of ultrafast ct ufct cardiac images is demonstrated ufct multi slice cine imaging gives a series of tomographic slices covering the volume of the heart at a rate of 17 frames per second the complete volume data set can be modeled using equations of continuum theory and through regularization velocity vectors of both blood and tissue can be determined at each voxel in the volume the authors present a technique to determine the pressure distribution throughout the volume of the left ventricle using the computed velocity field a numerical algorithm is developed by discretizing the pressure poisson equation ppe which is based on the navier stokes equation the algorithm is evaluated using a mathematical phantom of known velocity and pressure couette flow it is shown that the algorithm based on the ppe can reconstruct the pressure distribution using only the velocity data furthermore the ppe is shown to be robust in the presence of noise the velocity field and pressure distribution derived from a ufct study of a patient are also presented

vertex operators arising from the homogeneous realization for we use the underlying fock space for the homogeneous vertex operator representation of the affine lie algebra to construct a family of vertex operators as an application an irreducible module for an extended affine lie algebra of type a n 1 coordinatized by a quantum torus q of 2 variables or 3 variables is obtained moreover this module turns out to be a highest weight module which is an analog of the basic module for affine lie algebras

phase unwrapping of mr phase images using poisson equation the authors have developed a technique based on a solution of the poisson equation to unwrap the phase in magnetic resonance mr phase images the method is based on the assumption that the magnitude of the inter pixel phase change is less than spl pi per pixel therefore the authors obtain an estimate of the phase gradient by wrapping the gradient of the original phase image the problem is then to obtain the absolute phase given the estimate of the phase gradient the least squares ls solution to this problem is shown to be a solution of the poisson equation allowing the use of fast poisson solvers the absolute phase is then obtained by mapping the ls phase to the nearest multiple of 2 k from the measured phase the proposed technique is evaluated using mr phase images and is proven to be robust in the presence of noise an application of the proposed method to the 3 point dixon technique for water and fat separation is demonstrated

two parameter quantum vertex representations via finite groups and the mckay correspondence we introduce two parameter quantum toroidal algebras of simply laced types and provide their group theoretic realization using finite subgroups of sl2 c via mckay correspondence in particular our construction contains a realization of the vertex representation of the two parameter quantum affine algebras of ade types

r matrix for the two parameter quantum superalgebra ur s osp 1 2n in this paper we construct the two parameter r matrix for the quantum superalgebra ur s osp 1 2n which provides a solution to the quantum yang baxter equation we also prove that the r matrix satisfies the hexagon identities

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

a bending energy model for measurement of cardiac shape deformity an approach to analyzing and quantifying the shape characteristics of the endocardial contour of the left ventricle of the heart is described the computation begins by finding the local curvature differences between the contour under consideration and the mean normal contour at each of 100 equidistant points the weighted square of these differences summed over a set of points is shown to be the regional or global bending energy required to deform the mean normal contour to the characteristic shape of the analyzed contour resampling smoothing and curvature computation issues are considered for the image derived digital contours that are used in the analysis experiments were performed on artificial contour data and data derived from contrast ventriculographic cv studies of humans it is also shown that the method has been adapted to measure endocardial shape form equilibrium radionuclide angiocardiography

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

drinfel d doubles and lusztig s symmetries of two parameter quantum groups we flnd the deflning structures of two parameter quantum groups ur s g corre sponding to the orthogonal and the symplectic lie algebras which are realized as drinfel d doubles we further investigate the environment conditions upon which the lusztig s sym metries exist between ur s g h i and its associated object u si1 ri1 g hji

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

twisted vertex representations of quantum affine algebras recent interests in quantum groups are stimulated by their marvelous relations with quantum yang baxter equations conformal field theory invariants of links and knots and q hypergeometric series besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q deformations or quantum analogues of known structures quantum groups were first defined by drinfeld 2 and jimbo 9 also see 4 as a q deformation of the universal enveloping algebras of the kacmoody algebras in the work of trigonometric solutions of yang baxter equations in the same spirit it was shown in 13 14 that there exists a 1 1 correspondence between the integrable highest weight representations of symmetrizable kac moody algebras and those of the corresponding quantum groups where both spaces have the same dimension in the case of generic q i e q is not a root of unity moreover one can be very explicit in the case of quantum gl n to write down the irreducible highest weight representations quantum affine algebras are the quantum groups associated to affine lie algebras following drinfeld s realization 3 of q analog of loop algebras the vertex representation of untwisted simply laced quantum affine algebras was constructed in frenkel jing 6 which is a q deformation of frenkel kac 7 and segal 15 construction in the theory of affine lie algebras subsequently the same was done for the quantum affine algebra of type b in 1 in the present work we construct vertex representations of quantum affine algebras twisted by an automorphism of the dynkin diagram which generalizes certain important cases in the ordinary twisted vertex operator calculus 5

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