three routes to the exact asymptotics for the one dimensional quantum walk we demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one coin quantum walk on the infinite line via the jacobi polynomials that arise in the path integral representation we calculate the asymptotics using a method that is significantly easier to use than the darboux method it also provides a single integral representation for the wavefunction that works over the full range of positions n including throughout the transitional range where the behaviour changes from oscillatory to exponential previous analyses of this system have run into difficulties in the transitional range because the approximations on which they were based break down here the fact that there are two different kinds of approach to this problem path integral versus schrodinger wave mechanics is ultimately a manifestation of the equivalence between the path integral formulation of quantum mechanics and the original formulation developed in the 1920s we also discuss how and why our approach is related to the two methods that have already been used to analyse these systems

youden index and the optimal threshold for markers with mass at zero the youden index is often used as a summary measure of the receiver operating characteristic curve it measures the effectiveness of a diagnostic marker and permits the selection of an optimal threshold value or cutoff point for the biomarker of interest some markers while basically continuous and positive have a spike or positive mass of probability at the value zero we provide a flexible modeling approach for estimating the youden index and its associated cutoff point for such spiked data and compare it with the standard empirical approach we show how this modeling approach can be adjusted to take covariate information into account this approach is applied to data on the coronary calcium score a marker for atherosclerosis published in 2007 by john wiley sons ltd

two dimensional quantum random walk we analyze several families of two dimensional quantum random walks the feasible region the region where probabilities do not decay exponentially with time grows linearly with time as is the case with one dimensional qrw the limiting shape of the feasible region is however quite different the limit region turns out to be an algebraic set which we characterize as the rational image of a compact algebraic variety we also compute the probability profile within the limit region which is essentially a negative power of the gaussian curvature of the same algebraic variety our methods are based on analysis of the space time generating function following the methods of pemantle and wilson j comb theory ser a 97 1 129 161 2002

construction of complete embedded self similar surfaces under mean curvature flow part i we carry out the first main step towards the construc tion of new examples of complete embedded self similar surfaces under mean curvature flow an approximate solution is obtained by taking two known examples of self similar surfaces and desin gularizing the intersection circle using an appropriately modified singly periodic scherk surface called the core using an inverse function theorem we show that for small boundary conditions on the core there is an embedded surface close to the core that is a solution of the equation for self similar surfaces this provides us with an adequate central piece to substitute for the intersection

accuracy and cost comparison in medical testing using sequential testing strategies the practice of sequential testing is followed by the evaluation of accuracy but not by the evaluation of cost this paper focuses on three logic rules for combining two sequences of tests believe the positive bp which diagnoses disease if any of two tests is positive believe the negative bn which diagnoses disease if any of two tests is negative and believe the extreme be which diagnoses disease if the first test is positive or after a first inconclusive test a second test is positive for disease comparisons of these strategies are provided in terms of accuracy using false positive rate sensitivity pairs that make up the maximum receiver operating characteristic curve and cost of testing defined as the proportion of subjects needing two tests to diagnose disease a method to incorporate the cost of testing into the definition of the optimal operating point is also presented the performance of the testing strategies is examined with respect to the ratio of standard deviations and the correlation between test results under the bivariate normal assumptions under all parameter settings the maximum receiver operating characteristic curve of the be strategy never performed worse than the bn and bp strategies the be strategy also had the lowest cost the use of body mass index and plasma glucose concentration to diagnose diabetes in pima indians was presented as a real world application the optimal operating points found by the bn and be strategies produce lower false positive rate values than the bp strategy for these data

reducing cost in sequential testing a limit of indifference approach in noninferiority studies a limit of indifference is used to express a tolerance in results such that the clinician would regard such results as being acceptable or not worse we applied this concept to a measure of accuracy the receiver operating characteristic roc curve for a sequence of tests we expressed a limit of indifference for the range of acceptable sensitivity values and examined the associated cost of testing within this range in doing so we generated the minimum cost maximum roc mcmroc curve which reflects the reduced sensitivity and cost of testing we compared the mcmroc and its associated cost curve between limits of indifference set to 0 999 a 0 1 reduction in true positive rate tpr 0 95 a 5 reduction in tpr and 1 no reduction in tpr the limit of indifference tended to have less of an effect on the mcmroc curves than on the associated cost curves that were greatly affected cost was reduced at high false positive rates fprs at higher limit of indifference 0 999 and at small fprs as the limit of indifference decreased 0 95 these patterns were also observed as applied to sequential strategies used to diagnose diabetes in the pima indians copyright 2013 john wiley sons ltd

diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling the two test two population model originally formulated by hui and walter for estimation of test accuracy and prevalence estimation assumes conditionally independent tests constant accuracy across populations and binomial sampling the binomial assumption is incorrect if all individuals in a population e g child care centre village in africa or a cattle herd are sampled or if the sample size is large relative to population size in this paper we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard moreover two tests are often applied simultaneously for the purpose of obtaining a joint testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly sequential versions of such strategies are often applied in order to reduce the cost of testing we thus discuss joint simultaneous and sequential testing strategies and inference for them using the developed methods we analyse two real and one simulated data sets and we compare hypergeometric and binomial based inferences our findings indicate that the posterior standard deviations for prevalence but not sensitivity and specificity based on finite population sampling tend to be smaller than their counterparts for infinite population sampling finally we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation

some integral inequalities for l operator and their applications on self shrinkers abstract in this paper we derive a reilly type inequality for the drifting laplacian operator l on a self shrinker of the mean curvature flow using this reilly type inequality we obtain some new poincare type inequalities not only on the self shrinker but more interestingly also on its boundary moreover we get some eigenvalue estimates for l operator on the compact self shrinker and its boundary and also make some global estimates on generalized mean curvature h on the boundary

one dimensional three state quantum walk we study a generalized hadamard walk in one dimension with three inner states the particle governed by the three state quantum walk moves in superposition both to the left and to the right according to the inner state in addition to these two degrees of freedom it is allowed to stay at the same position we calculate rigorously the wave function of the particle starting from the origin for any initial qubit state and show the spatial distribution of probability of finding the particle in contrast with the hadamard walk with two inner states on a line the probability of finding the particle at the origin does not converge to zero even after infinite time steps except special initial states this implies that the particle is trapped near the origin after a long time with high probability

uniqueness of self similar shrinkers with asymptotically conical ends in this paper we show the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order also we construct non rotationally symmetric self shrinking ends asymptotic to generalized cylinders with rate as fast as any given polynomial

twenty combinatorial examples of asymptotics derived from multivariate generating functions let a bf r bf r in mathbb n d be a d dimensional array of numbers for which the generating function f bf z sum bf r a bf r bf z bf r is meromorphic in a neighborhood of the origin for example f may be a rational multivariate generating function we discuss recent results that allow the effective computation of asymptotic expansions for the coefficients of f our purpose is to illustrate the use of these techniques on a variety of problems of combinatorial interest the survey begins by summarizing previous work on the asymptotics of univariate and multivariate generating functions next we describe the morse theoretic underpinnings of some new asymptotic techniques we then quote and summarize these results in such a way that only elementary analyses are needed to check hypotheses and carry out computations the remainder of the survey focuses on combinatorial applications such as enumeration of words with forbidden substrings edges and cycles in graphs polyominoes and descents in permutations after the individual examples we discuss three broad classes of examples namely functions derived via the transfer matrix method those derived via the kernel method and those derived via the method of lagrange inversion these methods have the property that generating functions derived from them are amenable to our asymptotic analyses and we describe further machinery that facilitates computations for these classes of examples